inclusive disjunction

logic

Also known as: alternation

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June 29, 2026

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In logic, an inclusive disjunction is a statement that is true if either or both of its constituent propositions are true. This is often represented by the symbol \u2228, meaning "or." It is distinct from an exclusive disjunction, which is only true if one proposition is true, but not both.1

A truth table can illustrate the concept. For example, if 'p' and 'q' are propositions, the statement 'p \u2228 q' is false only when both 'p' and 'q' are false. In all other combinations (true-true, true-false, false-true), the inclusive disjunction is true. This logical operator is fundamental in understanding complex statements and arguments.21

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history of logic
The Megarians and the Stoics
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 terms of others.
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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 terms of others.
Read More

disjunction
…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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…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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