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| − | The logical operation of formation of the statement "A or B" from two statements <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332601.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332602.png" />. In formalized languages the disjunction of two statements <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332603.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332604.png" /> is denoted by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332605.png" />. The statements <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332606.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332607.png" /> are called the disjunctive terms of the statement <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d0332608.png" />. The meaning of the disjunction can be expressed by 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/d/d033/d033260/d0332609.png" /></td> <td colname="2" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d03326010.png" /></td> <td colname="3" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033260/d03326011.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">T</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">T</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 of formation of the statement "A or B" from two statements $A$ and $B$. In formalized languages the disjunction of two statements $A$ and $B$ is denoted by $A\lor B$. The statements $A$ and $B$ are called the disjunctive terms of the statement $A\lor B$. The meaning of the disjunction can be expressed by the following [[Truth table|truth table]]: |
| | | | |
| − | </td></tr> </table> | + | <center> |
| | + | {| border="1" class="wikitable" style="text-align:center; width:300px;" |
| | + | |$A$||$B$||$A\lor B$ |
| | + | |- |
| | + | |$T$||$T$||$T$ |
| | + | |- |
| | + | |$T$||$F$||$T$ |
| | + | |- |
| | + | |$F$||$T$||$T$ |
| | + | |- |
| | + | |$F$||$F$||$F$ |
| | + | |} |
| | + | </center> |
Latest revision as of 07:30, 12 August 2014
The logical operation of formation of the statement "A or B" from two statements $A$ and $B$. In formalized languages the disjunction of two statements $A$ and $B$ is denoted by $A\lor B$. The statements $A$ and $B$ are called the disjunctive terms of the statement $A\lor B$. The meaning of the disjunction can be expressed by the following truth table:
| $A$ |
$B$ |
$A\lor B$
|
| $T$ |
$T$ |
$T$
|
| $T$ |
$F$ |
$T$
|
| $F$ |
$T$ |
$T$
|
| $F$ |
$F$ |
$F$
|
How to Cite This Entry:
Disjunction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Disjunction&oldid=32851
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article