{"id":76,"date":"2026-02-18T10:13:33","date_gmt":"2026-02-18T08:13:33","guid":{"rendered":"https:\/\/blog.edu.turku.fi\/allu\/?page_id=76"},"modified":"2026-04-10T14:48:08","modified_gmt":"2026-04-10T11:48:08","slug":"logiikka","status":"publish","type":"page","link":"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/logiikka\/","title":{"rendered":"Logiikka"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" href=\"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/\" style=\"background-color:#d6d6ff\">Palaa takaisin<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color wp-elements-741cae579ed3853de7890e8c0e5d64b2\" style=\"color:#4e56b1\"><strong>Logiikka<\/strong><\/h2>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoon, perus ja vaikeaan<\/p>\n\n\n\n<div style=\"height:16px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#e6f3b0\">Helppo<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#d6d6ff\">Perus<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#fcd8c8\">Vaikea<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Teorian ymm\u00e4rt\u00e4minen on erityisen t\u00e4rke\u00e4\u00e4 logiikassa.<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-1&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-1-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-1\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Teoria<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-1\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-1-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/04\/Logiikka.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Tiedoston Logiikka upotus.\"><\/object><a id=\"wp-block-file--media-5bf39f81-cdb7-4153-a7c6-66ed5668ae73\" href=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/04\/Logiikka.pdf\">Logiikka<\/a><a href=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/04\/Logiikka.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-5bf39f81-cdb7-4153-a7c6-66ed5668ae73\">Lataa<\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:47px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-de28b11058836b2e3c98fd347e6f0698\" style=\"font-size:18px\">T\u00e4rkeimm\u00e4t termit:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Konnektiivien symbolit <\/strong>= \u00ac, \u2227, \u2228, \u21d2 ja \u21d4.<\/li>\n\n\n\n<li><strong>Formalisointi <\/strong>= Sanallinen lause muutetaan loogiseksi lauseeksi.<\/li>\n\n\n\n<li><strong>Totuustaulukko<\/strong> = Taulukko, joka esitt\u00e4\u00e4 kaikki mahdolliset totuusarvot (eli 1 tai 0).<\/li>\n\n\n\n<li><strong>V\u00e4itelause = propositio <\/strong>= Lyhyit\u00e4 lauseita, joilla on totuusarvo eli ovat joko tosia tai ep\u00e4tosia.<\/li>\n\n\n\n<li><strong>Atomilause<\/strong> = Lause logiikassa, jossa ei ole konnektiiveja.<\/li>\n\n\n\n<li><strong>Yhdistetty lause<\/strong> = Atomilauseista konnektiivien avulla muodostettu lause.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-768a665f0fbec0c7f41233ab39036d5c\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 1<\/strong><\/p>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-fff6b7cfb174d1ec84d78c024f90c306\" style=\"font-size:18px\"><strong>a)<\/strong> Kirjoita nelj\u00e4 virkett\u00e4.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Virke, jossa kerrot olevasi abi.<\/li>\n\n\n\n<li>Virke, jossa kiell\u00e4t olevasi abi.<\/li>\n\n\n\n<li>Virke, jossa kerrot, ett\u00e4 jos olet abi, niin k\u00e4yt lukiota.<\/li>\n\n\n\n<li>Virke, jossa kerrot, ett\u00e4 olet abi, jos ja vain jos teet ylioppilaskokeita<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-2&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b0\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-2-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-2\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-2\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-2-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Kirjoita siis mahdollisimman yksinkertaisesti, eik\u00e4 esimerkiksi \u201dEn siis todellakaan ole miss\u00e4\u00e4n nimess\u00e4 abi\u201d. Jos et ymm\u00e4rr\u00e4 teht\u00e4v\u00e4nantoa, katso vastaus ja p\u00e4\u00e4ttele seuraava osa itse.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-3&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b0\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-3-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-3\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-3\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-3-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ol class=\"wp-block-list\">\n<li>Olen abi<\/li>\n\n\n\n<li>En ole abi<\/li>\n\n\n\n<li>Jos olen abi niin k\u00e4yn lukiota<\/li>\n\n\n\n<li>Olen abi, jos ja vain jos teen ylioppilaskokeita.<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-72c76082cb54238bf94d6eb3cc653bb4\" style=\"font-size:18px\"><strong>b)<\/strong> Tee virkkeist\u00e4 atomilauseet A, B ja C.<\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-4&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b0\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-4-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-4\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-4\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-4-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>J\u00e4t\u00e4 virkkeist\u00e4 pois konnektiivit ei, ja, tai, jos\u2026niin sek\u00e4 jos ja vain jos.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-5&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b0\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-5-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-5\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-5\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-5-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>A = &#8221;olen abi&#8221;<br>B = &#8221;k\u00e4yn lukiota&#8221;<br>C = &#8221;teen ylioppilaskokeita&#8221;<\/p>\n\n\n\n<p>Virke \u201den ole abi\u201d voidaan esitt\u00e4\u00e4 atomilauseen A avulla, joten sit\u00e4 varten ei tarvita erillist\u00e4 kirjainta. Atomilauseet merkit\u00e4\u00e4n kirjaimilla, eik\u00e4 niiss\u00e4 k\u00e4ytet\u00e4 loogisia konnektiiveja.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-671ff201978b2848b767f10bdd45d077\" style=\"font-size:18px\"><strong>c) <\/strong>Formalisoi virkkeet k\u00e4ytt\u00e4en edellisen kohdan atomilauseita.<\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-6&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-5761dff279f8f863611cc636ae366b1b\" style=\"background-color:#e6f3b0\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-6-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-6\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-6\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-6-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Kertaa, mit\u00e4 konnektiivien symbolit ovat \u00ac, \u2227, \u2228, \u21d2 ja \u21d4, ja mit\u00e4 tarkoittaa formalisointi.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-7&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b0\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-7-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-7\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-7\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-7-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ol class=\"wp-block-list\">\n<li>A <\/li>\n\n\n\n<li>\u00ac A<\/li>\n\n\n\n<li>A \u21d2B<\/li>\n\n\n\n<li>A \u21d4 C<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-122ee762e85a69c3988fb828ed53ea3b\" style=\"font-size:18px\"><strong>d)<\/strong> Suomenna lauseet k\u00e4ytt\u00e4en b\u2011kohdassa m\u00e4\u00e4riteltyj\u00e4 atomilauseita.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>A \u02c4 B<\/li>\n\n\n\n<li>A \u02c5 B<\/li>\n<\/ol>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-8&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b0\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-8-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-8\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-8\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-8-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ol class=\"wp-block-list\">\n<li>Olen abi ja k\u00e4yn lukiota.<\/li>\n\n\n\n<li>Olen abi tai k\u00e4yn lukiota<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-de7f4c25b377e6276255da09d9018f16\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 2.<\/strong> Teht\u00e4v\u00e4st\u00e4 on perus ja vaikean tason versiot.<\/p>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-left has-black-color has-text-color has-background has-link-color wp-elements-bd939ef27fef10fcd89d5ef7bef7b724\" style=\"background-color:#fcd8c8;padding-right:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--20);font-size:18px\"><strong>\u00c4l\u00e4 viel\u00e4 pelaa perustason peli\u00e4 \u00e4l\u00e4k\u00e4 katso kuvaa !<\/strong><\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-black-color has-text-color has-link-color wp-elements-8d86246d42525ec9bf1d30c382a8a07c\" style=\"font-size:18px\"><strong>a) <\/strong>Muodosta todistajan lausunnosta atomilauseet ja rakenna niiden perusteella v\u00e4itelauseet. Formalisoi v\u00e4itelause atomilauseiden ja lausunnon sis\u00e4ll\u00f6n perusteella valitun loogisen konnektiivin avulla. Sievenn\u00e4 formalisoitu lause k\u00e4ytt\u00e4m\u00e4ll\u00e4 loogisia lakeja ja ilmaise lopuksi sievennetty v\u00e4itelause suomeksi. Jokainen tapaus k\u00e4sitell\u00e4\u00e4n erikseen.<\/p>\n\n\n\n<p>Todistajan lausunnot:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Kun ajattelen tarkemmin, ei ole niin, ett\u00e4 h\u00e4nell\u00e4 ei olisi p\u00e4\u00e4hinett\u00e4.<\/li>\n\n\n\n<li>Muistelisin, ettei ole totta, ett\u00e4 h\u00e4nell\u00e4 olisi ollut sek\u00e4 silm\u00e4lasit ett\u00e4 viikset.<\/li>\n\n\n\n<li>Muistikuvani mukaan h\u00e4nell\u00e4 oli p\u00e4\u00e4hine tai koruja. Jos oikein mietin mahdollisesti oli molemmat.<\/li>\n\n\n\n<li>Tatuointien ja p\u00e4\u00e4hineen v\u00e4lill\u00e4 oli selv\u00e4 yhteys, sill\u00e4 tatuoinnit eiv\u00e4t koskaan esiintyneet yksin. Aina kun tatuointeja n\u00e4kyi, h\u00e4nell\u00e4 oli my\u00f6s p\u00e4\u00e4hine. Lis\u00e4ksi on mahdollista, ettei h\u00e4nell\u00e4 ollut kumpaakaan tai pelkk\u00e4 p\u00e4\u00e4hine.<\/li>\n\n\n\n<li>Ep\u00e4illyll\u00e4 oli hiukset ja silm\u00e4lasit yht\u00e4 aikaa tai ei kumpaakaan.<\/li>\n<\/ol>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-fe9cc265 wp-block-group-is-layout-flex\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group alignwide is-vertical is-layout-flex wp-container-core-group-is-layout-fe9cc265 wp-block-group-is-layout-flex\">\n<div class=\"wp-block-group is-vertical is-content-justification-left is-layout-flex wp-container-core-group-is-layout-dd225191 wp-block-group-is-layout-flex\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-content-justification-left is-layout-constrained wp-container-core-group-is-layout-12dd3699 wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group alignfull is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-9&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-9-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-9\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-9\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-9-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-fe9cc265 wp-block-group-is-layout-flex\">\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Atomilauseet<\/summary>\n<p>P = \u201dep\u00e4illyll\u00e4 on p\u00e4\u00e4hine\u201d<br>S = \u201dep\u00e4illyll\u00e4 on silm\u00e4lasit\u201d<br>V = \u201dep\u00e4illyll\u00e4 on viikset\u201d<br>K = \u201dep\u00e4illlyll\u00e4 on koruja\u201d<br>P = \u201dep\u00e4illyll\u00e4 on p\u00e4\u00e4hine\u201d<br>T = \u201dep\u00e4illyll\u00e4 on tatuointeja\u201d<br>H = \u201dep\u00e4illyll\u00e4 on hiukset\u201d<br>S = \u201dep\u00e4illyll\u00e4 on silm\u00e4lasit\u201d<\/p>\n<\/details>\n<\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Loogiset lauseet<\/summary>\n<p>Vastaukset on <strong>paksunnettuna<\/strong><\/p>\n\n\n\n<p>1.<\/p>\n\n\n\n<p>V\u00e4itelause:  \u201dEi ole niin, ett\u00e4 ep\u00e4illyll\u00e4 ei ole p\u00e4\u00e4hinett\u00e4\u201d<br>Formalisoituna:  \u00ac(\u00acP)<br>Kaksoisnegaation laki: \u00ac(\u00acP) = <strong>P<\/strong><br>V\u00e4itelause lain soveltamisen j\u00e4lkeen: <strong>\u201dEp\u00e4illyll\u00e4 on p\u00e4\u00e4hine\u201d<\/strong><\/p>\n\n\n\n<p>2. <\/p>\n\n\n\n<p>V\u00e4itelause: \u201dEi ole niin, ett\u00e4 ep\u00e4illyll\u00e4 on silm\u00e4lasit ja viikset\u201d\u00ac (S \u2227 V)<br>Formalisoituna:  \u00ac (S \u2227 V)<br>De Morganin laki: \u00ac (S \u2227 V) = <strong>\u00acS \u2228 \u00acV<\/strong><br>V\u00e4itelause lain soveltamisen j\u00e4lkeen: <strong>\u201dEp\u00e4illyll\u00e4 ei ole silm\u00e4laseja tai ei ole viiksi\u00e4\u201d<\/strong><\/p>\n\n\n\n<p>3.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>V\u00e4itelause:  \u201dEi ole niin, ett\u00e4 ep\u00e4illyll\u00e4 on p\u00e4\u00e4hine tai koruja\u201d<br>Formalisoituna: \u00ac (P \u2228 K)<br>De Morganin laki: \u00ac (P \u2228 K) = <strong>\u00acP \u2227 \u00acK<\/strong><br>Looginen lause sanallisesti lain j\u00e4lkeen: <strong>\u201dEp\u00e4illyll\u00e4 ei ole p\u00e4\u00e4hinett\u00e4 ja ei ole koruja\u201d<\/strong><\/p>\n\n\n\n<p>4. <\/p>\n\n\n\n<p>V\u00e4itelause: <strong>\u201dJos ep\u00e4illyll\u00e4 on tatuointeja, niin ep\u00e4ilyll\u00e4 on p\u00e4\u00e4hine\u201d<\/strong><br>Formalisoituna: <strong>T \u21d2 P<\/strong><br><\/p>\n\n\n\n<p>5. <\/p>\n\n\n\n<p><br>V\u00e4itelause:  <strong>\u201dEp\u00e4ilyll\u00e4 on hiuksia, jos ja vain jos h\u00e4nell\u00e4 on silm\u00e4lasit.\u201d<\/strong><br>V\u00e4itelause:  <strong>H \u21d4 S<\/strong><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:18px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-2654041edeec04ff7709bb61e77a9afa\" style=\"font-size:18px\"><strong>b)<\/strong> Oleta, ettet tied\u00e4 hahmojen ominaisuuksia etuk\u00e4teen. P\u00e4\u00e4ttele totuustaulukoiden avulla, mitk\u00e4 ominaisuudet ep\u00e4illyill\u00e4 on. T\u00e4m\u00e4n j\u00e4lkeen vertaile sopiiko n\u00e4m\u00e4 perustason teht\u00e4v\u00e4n 2 kuvaselityksen hahmoihin.<\/p>\n\n\n\n<p style=\"font-size:18px\">Seuraavassa teht\u00e4v\u00e4n vastauksessa on selitettyn\u00e4, miksi teht\u00e4v\u00e4nanto on muotoiltuna n\u00e4in.<\/p>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-10&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"border-style:none;border-width:0px;background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-10-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-10\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-10\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-10-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Totuusarvot<\/summary>\n<p><strong>Hahmo 1 (numero 1)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P = 1<\/li>\n\n\n\n<li>V = 1<\/li>\n\n\n\n<li>T = 1<\/li>\n<\/ul>\n\n\n\n<p><strong>&nbsp;Hahmo 2 (numero 2)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>H = 1<\/li>\n\n\n\n<li>K = 1<\/li>\n\n\n\n<li>S = 1<\/li>\n<\/ul>\n\n\n\n<p><strong>Hahmo 3 (numero 3)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>H = 1<\/li>\n\n\n\n<li>S = 1<\/li>\n\n\n\n<li>T = 1<\/li>\n<\/ul>\n\n\n\n<p><strong>Hahmo 4 (numero 4)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P = 1<\/li>\n\n\n\n<li>K = 1<\/li>\n<\/ul>\n<\/details>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Totuustaulukoilla<\/summary>\n<p>1.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>P<\/td><td>\u00acP<\/td><td>\u00ac (\u00acP)<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Lause on tosi, kun P on tosi eli kun ep\u00e4illyll\u00e4 on p\u00e4\u00e4hine. Hamoilla 1 ja 4 on p\u00e4\u00e4hine, mink\u00e4 takia he ovat ep\u00e4iltyj\u00e4.<\/p>\n\n\n\n<p>2.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>S<\/td><td>V<\/td><td>S \u2227 V<\/td><td>\u00ac (S \u2227 V)<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>\u00acS<\/td><td>\u00acV<\/td><td>\u00acS \u2228 \u00acV<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Totuustaulukoiden perusteella lause on ainoastaan ep\u00e4tosi, kun ep\u00e4illyill\u00e4 on silm\u00e4lasit ja viikset. Ep\u00e4illyt ovat kaikki.<\/p>\n\n\n\n<p>Hahmolla 1 on viikset, muttei silm\u00e4laseja. Hahmolla 2 ja hahmolla 3 ei ole viiksi\u00e4, mutta on silm\u00e4lasit. Hahmolla 4 ei ole viiksi\u00e4, eik\u00e4 silm\u00e4laseja.<\/p>\n\n\n\n<p>3. <\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>P<\/td><td>K<\/td><td>P \u2228 K<\/td><td>\u00ac (P \u2228 K)<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>\u00acP<\/td><td>\u00acK<\/td><td>\u00acP \u2227 \u00acK<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Totuustaulukoiden perusteella ainoastaan, kun \u00acP ja \u00acK ovat tosia, lause on tosi. Eli ep\u00e4illyll\u00e4 ei saa olla p\u00e4\u00e4hinett\u00e4, eik\u00e4 koruja. Ep\u00e4ilty on hahmo 3.<\/p>\n\n\n\n<p>4. <\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>T<\/td><td>P<\/td><td>T \u21d2 P<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Lause on ainoastaan ep\u00e4tosi, kun ep\u00e4illyll\u00e4 on tatuointeja, mutta ei ole p\u00e4\u00e4hinett\u00e4. Tarkemmin lause on tosi, kun henkil\u00f6ll\u00e4 on tatuointeja ja p\u00e4\u00e4hine, pelkk\u00e4 p\u00e4\u00e4hine tai ei ole kumpaakaan. Ep\u00e4illyt ovat hahmo 1, hahmo 2 ja hahmo 4. <\/p>\n\n\n\n<p>Hahmolla 1 on sek\u00e4 tatuoinnit ett\u00e4 p\u00e4\u00e4hine, hahmolla 2 ei ole kumpaakaan ja hahmolla 4 on p\u00e4\u00e4hine ilman tatuointeja. <\/p>\n\n\n\n<p>5.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>T<\/td><td>P<\/td><td>T \u21d4 P<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<br><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Totuustaulukoiden perusteella lause on tosi, kun molemmat ovat tosia tai molemmat ovat ep\u00e4tosia. Eli ep\u00e4illyll\u00e4 on tatuointeja ja p\u00e4\u00e4hine tai ei kumpaakaan. Ep\u00e4illyt ovat kaikki. <\/p>\n\n\n\n<p>Hahmolla 1 ei ole hiuksia eik\u00e4 silm\u00e4laseja, hahmolla 2  on hiukset ja silm\u00e4lasit, hahmolla 3 on hiukset ja silm\u00e4lasit ja hahmolla 4  ei ole hiuksia eik\u00e4 silm\u00e4laseja. <\/p>\n<\/details>\n\n\n\n<p><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-555cd787ae8a8d44ff42f4594e9a22e6\" style=\"font-size:18px\"><strong>c)<\/strong> Tuomari on m\u00e4\u00e4r\u00e4nnyt kyseiset henkil\u00f6t syyllisiksi. Onko kukaan ep\u00e4illyist\u00e4 syyllinen? Tied\u00e4t nyt hahmojen ominaisuuksien totuusarvot.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>P \u2227 S<\/li>\n\n\n\n<li>\u00ac S \u2227 \u00ac T<\/li>\n\n\n\n<li>K \u21d2 S<\/li>\n\n\n\n<li>(K \u2228 V) \u2227 P<\/li>\n\n\n\n<li>(S \u2228 K) \u2227 \u00ac (V \u2228 T)<\/li>\n<\/ol>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-11&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"border-style:none;border-width:0px;background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-11-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-11\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-11\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-11-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>T\u00e4m\u00e4 l\u00e4hestymistapa helpottaa syyllisen selvitt\u00e4mist\u00e4. Edellisess\u00e4 teht\u00e4v\u00e4ss\u00e4 teht\u00e4v\u00e4nanto oli tarkoituksella monimutkaisempi, jotta ratkaisu perustui ensin totuustaulukon muodostamiseen ja vasta sen j\u00e4lkeen hahmojen 1\u20134 tunnistamiseen. T\u00e4ss\u00e4 teht\u00e4v\u00e4ss\u00e4 hahmojen totuusarvot tiedet\u00e4\u00e4n valmiiksi, mik\u00e4 tekee teht\u00e4v\u00e4st\u00e4 nopeamman ratkaista.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>P \u2227 S<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Hahmo<\/td><td>P<\/td><td>S<\/td><td>P \u2227 S<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>2<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>3<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>4<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Kukaan ei ole syyllinen.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2. \u00ac S \u2227 \u00ac T<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Hahmo<\/td><td>S<\/td><td>\u00acS<\/td><td>T<\/td><td>\u00acT<\/td><td>\u00acS \u2227 \u00acT<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>2<\/td><td>1<\/td><td>0<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>3<\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>4<\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Hahmo 4 on syyllinen.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3. K \u21d2 S<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Hahmo<\/td><td>K<\/td><td>S<\/td><td>K \u21d2 S<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>2<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>3<\/td><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>4<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Hahmot 1\u20133 ovat syyllisi\u00e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4. (K \u2228 V) \u2227 P<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Hahmo<\/td><td>K<\/td><td>V<\/td><td>K \u2228 V<\/td><td>P<\/td><td>(K \u2228 V) \u2227 P<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>2<\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>3<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>4<\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Hahmot 1 ja 4 ovat syyllisi\u00e4<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5. (S \u2228 K) \u2227 \u00ac (V \u2228 T)<\/li>\n<\/ul>\n\n\n\n<p>S \u2228 K<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Hahmo<\/td><td>S<\/td><td>K<\/td><td>S \u2228 K<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>2<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>3<\/td><td>1<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>4<\/td><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-left\"><code>       <\/code>\u00ac (V \u2228 T):<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Hahmo<\/td><td>V<\/td><td>T<\/td><td>V \u2228 T<\/td><td>\u00ac (V \u2228 T)<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>2<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>3<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>4<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><code>     <\/code>(S \u2228 K) \u2227 \u00ac (V \u2228 T)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Hahmo<\/td><td>S \u2228 K<\/td><td>\u00ac (V \u2228 T)<\/td><td>(S \u2228 K) \u2227 \u00ac (V \u2228 T)<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>2<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>3<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>4<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Hahmot 2 ja 4 ovat syyllisi\u00e4.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:46px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group alignwide is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-12&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-12-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-12\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\"><strong>Teht\u00e4v\u00e4 2<\/strong>: Kuvaselitys tunnistamistilanteesta. Varmista, ett\u00e4 tulkitset kuvan hahmojen ominaisuudet samalla tavalla kuin kuvan laatija on tarkoittanut.<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-12\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-12-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><img decoding=\"async\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/a-1024x456.png\" alt=\"Hahmo 1 (hattu, viikset, tatuointi)\nHahmo 2 (hiukset, korvakorut, kaulakoru, silm\u00e4lasit)\n\nHahmo 3 (hiukset, silm\u00e4lasit, tatuointi)\nHahmo 4 (pipo, nen\u00e4l\u00e4vistys, kaulakoru)\n\"><\/p>\n\n\n\n<p><strong>Hahmo 1 (numero 1)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>hattu<\/li>\n\n\n\n<li>viikset<\/li>\n\n\n\n<li>tatuointi<\/li>\n<\/ul>\n\n\n\n<p><strong>&nbsp;Hahmo 2 (numero 2)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<ul class=\"wp-block-list\">\n<li>hiukset<\/li>\n\n\n\n<li>korvakorut ja kaulakoru<\/li>\n\n\n\n<li>silm\u00e4lasit<\/li>\n<\/ul>\n<\/div>\n\n\n\n<p><strong>Hahmo 3 (numero 3)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>hiukset<\/li>\n\n\n\n<li>silm\u00e4lasit<\/li>\n\n\n\n<li>tatuointi<\/li>\n<\/ul>\n\n\n\n<p><strong>Hahmo 4 (numero 4)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>nen\u00e4l\u00e4vistys ja kaulakoru<\/li>\n\n\n\n<li>pipo<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group alignwide is-layout-constrained wp-block-group-is-layout-constrained\">\n<details class=\"wp-block-details has-black-color has-text-color has-background has-link-color has-medium-font-size wp-elements-75b974ca8dc9f7eaf341a648031f0960 is-layout-flow wp-block-details-is-layout-flow\" style=\"background-color:#d6d6ff\"><summary><strong>Teht\u00e4v\u00e4 2: <\/strong>Pelaa tunnistamistilanne<\/summary>\n<p>Ohje: Oikeita vastauksia voi olla useita ja valitse kaikki oikeat vastaukset. K\u00e4yt\u00e4 apuna totuustaulukoita lauseiden tulkitsemiseen. \u00c4l\u00e4 p\u00e4\u00e4ttele vastausta pelk\u00e4st\u00e4\u00e4n todistajan lausunnon perusteella. Totuustaulukoiden oikeat vastaukset l\u00f6ytyv\u00e4t vaikean version vastauksesta. Jokainen tapaus on oma erillinen tilanteensa.<\/p>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-15\" class=\"h5p-iframe\" data-content-id=\"15\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Logiikka_ep\u00e4illyt\"><\/iframe><\/div>\n\n\n\n<p>Peli on inspiroitu englanninkielisest\u00e4 logiikkapelist\u00e4: <a href=\"https:\/\/collegemathgames.com\/games\/connective-detective\/\">Connective Detective<\/a><\/p>\n<\/details>\n<\/div>\n\n\n\n<div style=\"height:46px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color has-medium-font-size wp-elements-188d6417b54859c696019f9d55597b60\"><strong>Teht\u00e4v\u00e4 3: Marsun hoito-ohjeet<\/strong><\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n\n\n\n<p>Jos marsu on pitk\u00e4karvainen niin turkin hoitaminen on vaativaa. Marsu tarvitsee lajitoverin, eik\u00e4 viihdy pitki\u00e4 aikoja itsekseen. Marsu on \u00e4\u00e4nek\u00e4s, jos ja vain jos se haluaa signaloida jotain. Jos marsua ei hoideta oikein niin se voi sairastua tai pahimmassa tapauksessa kuolla.<\/p>\n\n\n\n<div style=\"height:18px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-183063ca4b1a79f80c0eb7cbade4c30c\" style=\"font-size:18px\"><strong>a)<\/strong> Tee atomilauseita seuraavista virkkeist\u00e4. Atomilauseissa pit\u00e4\u00e4 k\u00e4yd\u00e4 selv\u00e4sti ilmi, ett\u00e4 v\u00e4itteet koskevat marsua.<\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-13&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-13-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-13\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-13\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-13-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Atomilauseita on yhdeks\u00e4n (A, B, C, D, E, F, G, H, I). Erottele, mitk\u00e4 sanat ovat konnektiiveja ja mitk\u00e4 atomilauseita. Etsi sanoja ja, ei, tai, jos&#8230; niin ja vain ja jos vain. Jos et ymm\u00e4rr\u00e4, mit\u00e4 t\u00e4ss\u00e4 haetaan, katso vinkki\u00e4 teht\u00e4v\u00e4st\u00e4 1.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-14&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-14-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-14\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-14\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-14-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><br>A = \u201dmarsu on pitk\u00e4karvainen\u201d<br>B = \u201dmarsun turkin hoitaminen on vaativaa\u201d<br>C= \u201dmarsu tarvitsee lajitoverin\u201d<br>D= \u201dmarsu viihtyy pitki\u00e4 aikoja itsekseen\u201d<br>E= \u201d marsu on \u00e4\u00e4nek\u00e4s\u201d<br>F = \u201dmarsu haluaa signaloida jotain\u201d<br>G= \u201dmarsua hoidetaan oikein \u201d<br>H= \u201dmarsu voi sairastua\u201d<br>I= \u201dmarsu voi pahimmassa tapauksessa kuolla\u201d<\/p>\n\n\n\n<p>Huomaa, ett\u00e4 \u201dei\u201d-sana j\u00e4tettiin atomilauseista pois, koska atomilauseessa ei saa k\u00e4ytt\u00e4\u00e4 loogista negaatiota. T\u00e4m\u00e4 helpottaa teht\u00e4vien tekemist\u00e4 ja tekee formalisoinnista selke\u00e4mp\u00e4\u00e4.<\/p>\n\n\n\n<p>Sanaa \u201dmarsu\u201d toistetaan atomilauseissa, koska atomilauseen pit\u00e4\u00e4 olla t\u00e4ysin yksiselitteinen ja ymm\u00e4rrett\u00e4v\u00e4 my\u00f6s silloin, kun se esiintyy yksin\u00e4\u00e4n ilman alkuper\u00e4ist\u00e4 virkett\u00e4. Atomilausetta ei voi j\u00e4tt\u00e4\u00e4 muotoon \u201dse haluaa signaloida jotain\u201d, koska pronomini \u201dse\u201d ei yksin\u00e4\u00e4n kerro, mihin v\u00e4ite viittaa. Teht\u00e4v\u00e4nannossa nimenomaan pyydettiin tekem\u00e4\u00e4n atomilauseet niin, ett\u00e4 niist\u00e4 k\u00e4y aina suoraan ilmi, ett\u00e4 kyseess\u00e4 on marsu.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-2dc2310f71b910387773b52627845f61\" style=\"font-size:18px\"><strong>b)<\/strong> Virkkeet ovat jo v\u00e4itelausemuodoissa valmiiksi. P\u00e4\u00e4telle virkkeiden sis\u00e4ll\u00f6n perusteella, mik\u00e4 looginen konnektiivi yhdistettyyn lauseeseen kuuluu. Formalisoi yhdistetyt lauseet.<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-15&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-15-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-15\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-15\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-15-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ol class=\"wp-block-list\">\n<li>Jos marsu on pitk\u00e4karvainen, niin turkin hoitaminen on vaativaa.\n<ul class=\"wp-block-list\">\n<li>A \u21d2 B<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Marsu tarvitsee lajitoverin, eik\u00e4 viihdy pitki\u00e4 aikoja itsekseen.\n<ul class=\"wp-block-list\">\n<li>C \u2227 \u00ac D<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Marsu on \u00e4\u00e4nek\u00e4s, jos ja vain jos haluaa signaloida jotain.\n<ul class=\"wp-block-list\">\n<li>E \u21d4 F<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Jos marsua ei hoideta oikein niin se voi sairastua tai pahimmassa tapauksessa kuolla.\n<ul class=\"wp-block-list\">\n<li>\u00ac G\u21d2 (H \u2228 I)<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-7cfd249b65261e99a557643927c0d5b4\" style=\"font-size:18px\"><strong>c)<\/strong> Milloin n\u00e4m\u00e4 lauseet ovat tosia? <\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-16&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-16-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-16\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-16\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-16-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Vinkki: Aloita kirjoittamalla totuustaulukkoon sarakkeet A, B ja tarvittaessa C.<br>N\u00e4ihin sarakkeisiin merkit\u00e4\u00e4n kaikki mahdolliset totuusarvoyhdistelm\u00e4t.<\/p>\n\n\n\n<p>Kun perussarakkeet on laadittu, tarkastele valitun konnektiivin totuustaulukkoa ja p\u00e4\u00e4ttele, miss\u00e4 kohdissa konnektiivin arvo on 1 (tosi) tai vaihtoehtoisesti 0 (ep\u00e4tosi).<br>N\u00e4iden perusteella t\u00e4yt\u00e4t konnektiiville oman sarakkeensa taulukkoon.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-17&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-17-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-17\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-17\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-17-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p class=\"has-medium-font-size\"><strong>1. <\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>A<\/td><td>B<\/td><td>A \u21d2 B<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Lause on ep\u00e4tosia ainoastaan, kun A on tosi ja B on ep\u00e4tosi. Suomennettuna jos marsu on pitk\u00e4karvainen niin turkin hoitaminen ei ole vaativaa.<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>2. <\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>C<\/td><td>D<\/td><td>\u00acD<\/td><td>C \u2227 \u00acD<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Lause on tosi ainoastaan, kun C ja \u00acD ovat tosia 1. Suomennettuna marsu tarvitsee lajitoverin ja ei viihdy pitki\u00e4 aikoja itsekseen<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>3. <\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>E<\/td><td>F<\/td><td>E \u21d4 F<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Lause on tosi, kun E  ja F ovat joko molemmat tosia tai ep\u00e4tosia. Ensimm\u00e4inen lause suomennettuna on marsu on \u00e4\u00e4nek\u00e4s vain ja jos vain se haluaa signaloida jotain. Toinen lause on suomennettuna marsu ei ole \u00e4\u00e4nek\u00e4s vain ja jos vain se ei halua signaloida jotain. <\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>4.<\/strong><\/p>\n\n\n\n<p>T\u00e4m\u00e4 on monimutkaisempi, koska muuttujia on kolme.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>G<\/td><td>H<\/td><td>I<\/td><td>(H \u2228 I)<\/td><td>\u00ac G<\/td><td>\u00ac G \u21d2 (H \u2228 I)<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Lause on ep\u00e4tosi kolmessa tapauksessa. N\u00e4iss\u00e4 G on tosi. Joko H tai I ovat ep\u00e4tosia tai molemmat ovat tosia. Suomennettuna n\u00e4m\u00e4 tapaukset ovat seuraavat:<\/p>\n\n\n\n<p>Jos marsua hoidetaan oikein niin se ei voi sairastua tai pahimmassa tapauksessa voi kuolla.<br>Jos marsua hoidetaan oikein niin se voi sairastua tai pahimmassa tapauksessa ei voi kuolla.<br>Jos marsua hoidetaan oikein niin se voi sairastua tai pahimmassa tapauksessa voi kuolla.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:48px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-17c31572023859ffe59e8aecaa6c2f99\" style=\"font-size:18px\"><strong>d)<\/strong> Suomenna n\u00e4iden perusteella seuraavat lauseet. <\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u00ac (A \u2228 B)<\/li>\n\n\n\n<li>\u00ac (A \u2227 B)<\/li>\n\n\n\n<li>\u00ac (\u00ac C)<\/li>\n\n\n\n<li>E \u21d4 (F \u2227 \u00ac G)<\/li>\n\n\n\n<li>\u00ac (\u00ac A \u21d4 \u00ac B)<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-18&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-18-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-18\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-18\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-18-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Oikeat vastaukset on lihavoitu.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u00ac (A \u2228 B)\n<ul class=\"wp-block-list\">\n<li>De Morganin laki \u00ac (A) \u2227 \u00ac (B): <strong>Marsu ei ole pitk\u00e4karvainen ja turkin hoitaminen ei ole vaativaa.<\/strong><\/li>\n\n\n\n<li>Ilman lakia: <strong>Ei ole niin, ett\u00e4 marsu on pitk\u00e4karvainen tai turkin hoitaminen on vaativaa.<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u00ac (A \u2227 B)\n<ul class=\"wp-block-list\">\n<li>De Morganin laki \u00ac (A) \u2228 \u00ac (B): <strong>Marsu ei ole pitk\u00e4karvainen tai turkin hoitaminen ei ole vaativaa.<\/strong><\/li>\n\n\n\n<li>Ilman lakia: <strong>Ei ole niin, ett\u00e4 marsu on pitk\u00e4karvainen ja turkin hoitaminen on vaativaa.<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u00ac (\u00ac C)\n<ul class=\"wp-block-list\">\n<li>Kaksoisnegaation laki C: <strong>Marsu tarvitsee lajitoverin.<\/strong><\/li>\n\n\n\n<li>Ilman lakia: <strong>Ei ole totta, ett\u00e4 marsu ei tarvitse lajitoveria.<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>E \u21d4 (F \u2227 \u00ac G)\n<ul class=\"wp-block-list\">\n<li><strong>Marsu on \u00e4\u00e4nek\u00e4s, jos ja vain jos se haluaa signaloida jotain ja marsua ei hoideta oikein\u00ad\u00ad\u00ad\u00ad\u00ad<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u00ac (\u00ac A \u21d4 \u00ac B)\n<ul class=\"wp-block-list\">\n<li><strong>Ei ole niin, ett\u00e4 marsu ei ole pitk\u00e4karvainen, jos ja vain jos turkin hoitaminen ei ole vaativaa.<\/strong><\/li>\n\n\n\n<li>Olisiko t\u00e4ss\u00e4 saanut muotoilla muotoon (A \u21d4 B) ? Tutkitaan asiaa seuraavassa kohdassa <\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-19&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-19-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-19\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Pohdinta vastausvaihtoehdosta 5<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-19\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-19-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<ul class=\"wp-block-list\">\n<li>Olisiko kohdassa viisi saanut muotoilla muotoon (A \u21d4 B)? Tutkitaan asiaa<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>A<\/td><td>B<\/td><td>\u00acA<\/td><td>\u00acB<\/td><td>(\u00acA \u21d4 \u00acB)<\/td><td>\u00ac (\u00acA \u21d4 \u00acB)<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><td>1<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>1<\/td><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>A<\/td><td>B<\/td><td>(A \u21d4 B)<\/td><\/tr><tr><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>0<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>1<\/td><td>0<\/td><\/tr><tr><td>0<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Lauseet eiv\u00e4t ole loogisesti ekvivalentit, koska totuustaulut eiv\u00e4t ole samat. Ei olisi saanut. <\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Logiikka Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoon, perus ja vaikeaan Teorian ymm\u00e4rt\u00e4minen on erityisen t\u00e4rke\u00e4\u00e4 logiikassa. T\u00e4rkeimm\u00e4t termit: Teht\u00e4v\u00e4 1 a) Kirjoita nelj\u00e4 virkett\u00e4. b) Tee virkkeist\u00e4 atomilauseet A, B ja C. c) Formalisoi virkkeet k\u00e4ytt\u00e4en edellisen kohdan atomilauseita. d)<\/p>\n","protected":false},"author":3429,"featured_media":0,"parent":4,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-76","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/76","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/users\/3429"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/comments?post=76"}],"version-history":[{"count":183,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/76\/revisions"}],"predecessor-version":[{"id":3222,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/76\/revisions\/3222"}],"up":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/4"}],"wp:attachment":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/media?parent=76"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}