# exclusive or

## English

Wikipedia has an article on:
Wikipedia
p q p exclusive or q
0 0 0
0 1 1
1 0 1
1 1 0

### Noun

exclusive or (plural exclusive ors)

1. () Exclusive disjunction: the use of or to indicate that of two predicates, one is true and one is false (without specifying which is which); contrasted with inclusive or, which does not imply that one must be false.
2. (logic, computing, more generally) Exclusive disjunction: the use of or to indicate that of two or more predicates, an odd number are true (without specifying which or how many); contrasted with inclusive or, which indicates only that one or more is true.
3. () An exclusive disjunction; the result of applying the above-described exclusive or to two or more predicates; contrasted with an inclusive or, which is the result of applying an inclusive or.

#### Usage notes

• (the result): In an expression of formal logic, the phrase exclusive or (or hyphenated as exclusive-or) may appear between the predicates, much like a conjunction:
(x ∧ ¬y) ${\displaystyle \lor }$xy) ↔ xy, which reads: x exclusive-or y.