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Difference between revisions of "Conjunction"

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The logical operation used for forming the expression  "A and B"  from two expressions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250801.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250802.png" />. In formalized languages, the conjunction of two expressions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250803.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250804.png" /> is denoted by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250805.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250806.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250807.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250808.png" />, or <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c0250809.png" />. The expressions <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c02508010.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c02508011.png" /> are called the conjunctive terms of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c02508012.png" />. The normal usage of the conjunction in mathematical logic corresponds to the following [[Truth table|truth table]]:''''''<table border="0" cellpadding="0" cellspacing="0" style="background-color:black;"> <tr><td> <table border="0" cellspacing="1" cellpadding="4" style="background-color:black;"> <tbody> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c02508013.png" /></td> <td colname="2" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c02508014.png" /></td> <td colname="3" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025080/c02508015.png" /></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">T</td> <td colname="2" style="background-color:white;" colspan="1">T</td> <td colname="3" style="background-color:white;" colspan="1">T</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">T</td> <td colname="2" style="background-color:white;" colspan="1">F</td> <td colname="3" style="background-color:white;" colspan="1">F</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">F</td> <td colname="2" style="background-color:white;" colspan="1">T</td> <td colname="3" style="background-color:white;" colspan="1">F</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">F</td> <td colname="2" style="background-color:white;" colspan="1">F</td> <td colname="3" style="background-color:white;" colspan="1">F</td> </tr> </tbody> </table>
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{{TEX|done}}
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The logical operation used for forming the expression  "A and B"  from two expressions $A$ and $B$. In formalized languages, the conjunction of two expressions $A$ and $B$ is denoted by $A\&B$, $A\land B$, $A\cap B$, $A\cdot B$, or $AB$. The expressions $A$ and $B$ are called the conjunctive terms of $A\&B$. The normal usage of the conjunction in mathematical logic corresponds to the following [[Truth table|truth table]]:
  
</td></tr> </table>
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<center>
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{| border="1" class="wikitable" style="text-align:center; width:300px;"
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|$A$||$B$||$A\&B$
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|-
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|$T$||$T$||$T$
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|-
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|$T$||$F$||$F$
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|-
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|$F$||$T$||$F$
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|-
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|$F$||$F$||$F$
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|}
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</center>

Latest revision as of 07:28, 12 August 2014

The logical operation used for forming the expression "A and B" from two expressions $A$ and $B$. In formalized languages, the conjunction of two expressions $A$ and $B$ is denoted by $A\&B$, $A\land B$, $A\cap B$, $A\cdot B$, or $AB$. The expressions $A$ and $B$ are called the conjunctive terms of $A\&B$. The normal usage of the conjunction in mathematical logic corresponds to the following truth table:

$A$ $B$ $A\&B$
$T$ $T$ $T$
$T$ $F$ $F$
$F$ $T$ $F$
$F$ $F$ $F$
How to Cite This Entry:
Conjunction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conjunction&oldid=11757
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article