Difference between revisions of "Exclusive disjunction"
From Encyclopedia of Mathematics
(Importing text file) |
(TeX) |
||
| Line 1: | Line 1: | ||
| − | One of the logical connectives. The proposition | + | {{TEX|done}} |
| + | 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 | ||
| − | + | $$A\dot\lor B\Leftrightarrow(A\lor B)\&\neg(A\land B).$$ | |
Revision as of 13:48, 17 March 2014
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
$$A\dot\lor B\Leftrightarrow(A\lor B)\&\neg(A\land B).$$
How to Cite This Entry:
Exclusive disjunction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Exclusive_disjunction&oldid=31389
Exclusive disjunction. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Exclusive_disjunction&oldid=31389
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article