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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> | + | {{TEX|done}} |
| | + | 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> | + | <center> |
| | + | {| border="1" class="wikitable" style="text-align:center; width:300px;" |
| | + | |$A$||$B$||$A\&B$ |
| | + | |- |
| | + | |$T$||$T$||$T$ |
| | + | |- |
| | + | |$T$||$F$||$F$ |
| | + | |- |
| | + | |$F$||$T$||$F$ |
| | + | |- |
| | + | |$F$||$F$||$F$ |
| | + | |} |
| | + | </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