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http:///mymemo.xyz/wiki/api.php?action=feedcontributions&feedformat=atom&user=2400%3A2412%3A9260%3A1100%3AD11C%3AD1FD%3A675C%3AD69B 2024-05-23T05:02:48Z 利用者の投稿記録 MediaWiki 1.31.0 2017-09-06T14:39:21Z

<p>2400:2412:9260:1100:D11C:D1FD:675C:D69B: </p> <hr /> <div>&#039;&#039;&#039;真理値表&#039;&#039;&#039;（しんりちひょう、Truth table）は、[[ブール関数|論理関数]]の、入力の全てのパターンとそれに対する結果の値を、表にしたものである。<br /> <br /> 例1：命題Pの[[否定]]「&lt;math&gt;\lnot P&lt;/math&gt;」の場合、以下のような真理値表になる。<br /> <br /> {| class=&quot;wikitable&quot;<br /> |- style=&quot;background-color:#cccccc&quot;<br /> ! 命題 &#039;&#039;P&#039;&#039; !! ¬&#039;&#039;P&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 真 || &#039;&#039;&#039;偽&#039;&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 偽 || &#039;&#039;&#039;真&#039;&#039;&#039;<br /> |}<br /> <br /> 例2：2つの命題P,Qの[[論理和]]「&lt;math&gt;P \lor Q&lt;/math&gt;」の場合、以下のような真理値表になる。<br /> <br /> {| class=&quot;wikitable&quot;<br /> |- style=&quot;background-color:#cccccc&quot;<br /> ! 命題 &#039;&#039;P&#039;&#039; !! 命題 &#039;&#039;Q&#039;&#039; !! &#039;&#039;P&#039;&#039; ∨ &#039;&#039;Q&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 真 || 真 || &#039;&#039;&#039;真&#039;&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 真 || 偽 || &#039;&#039;&#039;真&#039;&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 偽 || 真 || &#039;&#039;&#039;真&#039;&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 偽 || 偽 || &#039;&#039;&#039;偽&#039;&#039;&#039;<br /> |}<br /> <br /> 例3：2つの命題P,Qの[[論理積]]「&lt;math&gt;P \land Q&lt;/math&gt;」の場合、以下のような真理値表になる。<br /> <br /> {| class=&quot;wikitable&quot;<br /> |- style=&quot;background-color:#cccccc&quot;<br /> ! 命題 &#039;&#039;P&#039;&#039; !! 命題 &#039;&#039;Q&#039;&#039; !! &#039;&#039;P&#039;&#039; ∧ &#039;&#039;Q&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 真 || 真 || &#039;&#039;&#039;真&#039;&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 真 || 偽 || &#039;&#039;&#039;偽&#039;&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 偽 || 真 || &#039;&#039;&#039;偽&#039;&#039;&#039;<br /> |- align=&quot;center&quot;<br /> | 偽 || 偽 || &#039;&#039;&#039;偽&#039;&#039;&#039;<br /> |}<br /> <br /> なお、この表では「真」「偽」として表記してあるが、「T(=true)」「F(=false)」、「1」「0」の場合もあるし、「1」のみを記述して「0」を記述しない場合もある。<br /> {|class=wikitable style=&quot;text-align: center&quot;<br /> !P||Q||style=&quot;border-left: 2px solid #aaa&quot;|P∧Q||P∨Q||P⇒Q||¬P∧Q||P∨¬Q||¬(P∧Q)||¬P∨¬Q||¬(P∨Q)||¬P∧¬Q||¬P⇒Q||P∧¬Q<br /> |-<br /> |T||T||style=&quot;border-left: 2px solid #aaa&quot;|T||T||T||F||T||F||F||F||F||T||F<br /> |-<br /> |T||F||style=&quot;border-left: 2px solid #aaa&quot;|F||T||F||F||T||T||T||F||F||T||T<br /> |-<br /> |F||T||style=&quot;border-left: 2px solid #aaa&quot;|F||T||T||T||F||T||T||F||F||T||F<br /> |-<br /> |F||F||style=&quot;border-left: 2px solid #aaa&quot;|F||F||T||F||T||T||T||T||T||F||F<br /> |}<br /> <br /> == 関連項目 ==<br /> *[[真理値]]<br /> *[[カルノー図法]]<br /> *[[ブール代数]]<br /> *[[ブール関数]]<br /> *[[ベン図]]<br /> *[[選言標準形]]<br /> *[[連言標準形]]<br /> <br /> {{デフォルトソート:しんりちひよう}}<br /> [[category:表]]<br /> [[Category:論理学]]<br /> [[Category:命題論理]]<br /> [[Category:数学に関する記事]]</div>

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