exclusive disjunction

logic

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June 26, 2026

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Exclusive disjunction is a logical concept that is true only when one, but not both, of its constituent statements is true. This is distinct from inclusive disjunction, which is true if either or both of its constituent propositions are true. In logic, disjunction expresses the concept of "or" and presents alternatives. Exclusive disjunction is symbolized as x ⊻ y.123

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disjunction
For clarity, exclusive disjunction (either x or y, but not both), symbolized x ⊻ y, must be distinguished from inclusive disjunction (either x or y, or both x and y), symbolized x ∨ y. See also implication.
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For clarity, exclusive disjunction (either x or y, but not both), symbolized x ⊻ y, must be distinguished from inclusive disjunction (either x or y, or both x and y), symbolized x ∨ y. See also implication.
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history of logic
The Megarians and the Stoics
…disjunct is true (the modern “exclusive” disjunction). They also knew “inclusive” disjunction (defined as true when at least one disjunct is true), but this was not widely used. More important, the Stoics seem to have been the first to show how some of these truth-functional words may be defined in…
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…disjunct is true (the modern “exclusive” disjunction). They also knew “inclusive” disjunction (defined as true when at least one disjunct is true), but this was not widely used. More important, the Stoics seem to have been the first to show how some of these truth-functional words may be defined in…
Read More