Difference between revisions of "Exclusive disjunction"
From Encyclopedia of Mathematics
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| − | One of the logical connectives. The proposition $A\dot\lor B$, obtained from two propositions $A$ and $B$ using the exclusive disjunction $\dot\lor$, is taken to be true if $A$ is true and $B$ is false, or if $A$ is false and $B$ is true. In the remaining cases it is taken to be false. Thus, the exclusive disjunction can be expressed in terms of the ordinary (non-exclusive) disjunction by the formula | + | One of the logical connectives. The proposition $A\mathbin{\dot\lor}B$, obtained from two propositions $A$ and $B$ using the exclusive disjunction $\dot\lor$, is taken to be true if $A$ is true and $B$ is false, or if $A$ is false and $B$ is true. In the remaining cases it is taken to be false. Thus, the exclusive disjunction can be expressed in terms of the ordinary (non-exclusive) disjunction by the formula |
| − | + | \[A\mathbin{\dot\lor}B\Leftrightarrow(A\lor B)\mathbin\&\neg(A\land B).\] | |
Latest revision as of 13:49, 30 December 2018
One of the logical connectives. The proposition $A\mathbin{\dot\lor}B$, obtained from two propositions $A$ and $B$ using the exclusive disjunction $\dot\lor$, is taken to be true if $A$ is true and $B$ is false, or if $A$ is false and $B$ is true. In the remaining cases it is taken to be false. Thus, the exclusive disjunction can be expressed in terms of the ordinary (non-exclusive) disjunction by the formula
\[A\mathbin{\dot\lor}B\Leftrightarrow(A\lor B)\mathbin\&\neg(A\land B).\]
How to Cite This Entry:
Exclusive disjunction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Exclusive_disjunction&oldid=43573
Exclusive disjunction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Exclusive_disjunction&oldid=43573
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article