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	<updated>2026-04-11T20:31:14Z</updated>
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	<entry>
		<id>https://blackwiki.org/index.php?title=Template:Logic_functions&amp;diff=7137587</id>
		<title>Template:Logic functions</title>
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		<updated>2011-09-12T08:45:41Z</updated>

		<summary type="html">&lt;p&gt;213.88.148.34: typos (iff -&amp;gt; if)&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{| class=&amp;quot;wikitable&amp;quot; style=&amp;quot;text-align:center; margin: 1em auto 1em auto&amp;quot;&lt;br /&gt;
|- &lt;br /&gt;
!rowspan=2 |''INPUT''|| A&lt;br /&gt;
!width=20|0&lt;br /&gt;
!width=20|0&lt;br /&gt;
!width=20|1&lt;br /&gt;
!width=20|1&lt;br /&gt;
|rowspan=2 |&amp;lt;!-- Empty col --&amp;gt;&lt;br /&gt;
!rowspan=2 | Meaning&lt;br /&gt;
|-&lt;br /&gt;
! B || 0 || 1 || 0 || 1&lt;br /&gt;
&lt;br /&gt;
|- &lt;br /&gt;
|colspan=8|&amp;lt;!-- Empty line --&amp;gt;&lt;br /&gt;
|-&lt;br /&gt;
!rowspan=16 | ''OUTPUT'' &lt;br /&gt;
| FALSE || 0 || 0 || 0 || 0&lt;br /&gt;
|rowspan=16 |&lt;br /&gt;
|align=left|Whatever ''A'' and ''B'', the output is false. [[Contradiction_(logic)|Contradiction]].&lt;br /&gt;
|- &lt;br /&gt;
| A AND B || 0 || 0 || 0 || 1&lt;br /&gt;
|align=left|Output is true if and only if ([[if]]) both ''A'' and ''B'' are true.&lt;br /&gt;
|-&lt;br /&gt;
| A &amp;lt;math&amp;gt;\not\rightarrow&amp;lt;/math&amp;gt; B || 0 || 0 || 1 || 0&lt;br /&gt;
|align=left|''A'' [[Material nonimplication|doesn't imply]] ''B''. True if ''A'' but not ''B''.&lt;br /&gt;
|-&lt;br /&gt;
| A || 0 || 0 || 1 || 1&lt;br /&gt;
|align=left|True whenever ''A'' is true.&lt;br /&gt;
|-&lt;br /&gt;
| A &amp;lt;math&amp;gt;\not\leftarrow&amp;lt;/math&amp;gt; B|| 0 || 1 || 0 || 0&lt;br /&gt;
|align=left|''A'' [[Converse nonimplication|is not implied by]] ''B''. True if not ''A'' but ''B''.&lt;br /&gt;
|- &lt;br /&gt;
| B || 0 || 1 || 0 || 1&lt;br /&gt;
|align=left|True whenever ''B'' is true.&lt;br /&gt;
|- &lt;br /&gt;
| A XOR B || 0 || 1 || 1 || 0&lt;br /&gt;
|align=left|True if ''A'' is not equal to ''B''.&lt;br /&gt;
|- &lt;br /&gt;
| A OR B || 0 || 1 || 1 || 1&lt;br /&gt;
|align=left|True if ''A'' is true, or ''B'' is true, or both.&lt;br /&gt;
|- &lt;br /&gt;
| A NOR B || 1 || 0 || 0 || 0&lt;br /&gt;
|align=left|True if neither ''A'' nor ''B''.&lt;br /&gt;
|- &lt;br /&gt;
| A XNOR B || 1 || 0 || 0 || 1&lt;br /&gt;
|align=left|True if ''A'' is equal to ''B''.&lt;br /&gt;
|- &lt;br /&gt;
| NOT B || 1 || 0 || 1 || 0&lt;br /&gt;
|align=left|True if ''B'' is false.&lt;br /&gt;
|- &lt;br /&gt;
| A &amp;lt;math&amp;gt;\leftarrow&amp;lt;/math&amp;gt; B|| 1 || 0 || 1 || 1&lt;br /&gt;
|align=left|''A'' [[Converse implication|is implied by]] ''B''. False if not ''A'' but ''B'', otherwise true.&lt;br /&gt;
|- &lt;br /&gt;
| NOT A || 1 || 1 || 0 || 0&lt;br /&gt;
|align=left|True if ''A'' is false.&lt;br /&gt;
|- &lt;br /&gt;
| A &amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt; B || 1 || 1 || 0 || 1&lt;br /&gt;
|align=left|''A'' [[Material conditional|implies]] ''B''. False if ''A'' but not ''B'', otherwise true.&lt;br /&gt;
|- &lt;br /&gt;
| A NAND B || 1 || 1 || 1 || 0&lt;br /&gt;
|align=left|''A'' and ''B'' are not both true.&lt;br /&gt;
|- &lt;br /&gt;
| TRUE || 1 || 1 || 1 || 1&lt;br /&gt;
|align=left|Whatever ''A'' and ''B'', the output is true. [[Tautology_(logic)|Tautology]].&lt;br /&gt;
|}&amp;lt;noinclude&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics templates|{{PAGENAME}}]]&lt;br /&gt;
[[Category:WikiProject Logic]]&lt;br /&gt;
&amp;lt;/noinclude&amp;gt;&lt;/div&gt;</summary>
		<author><name>213.88.148.34</name></author>
		
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