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A disjunction is a sequence of sentences separated by occurrences of the ∨ operator and enclosed in parentheses. For example, we can write the disjunction of p and q as (p ∨ q).
The constituent sentences of a disjunction are called disjuncts. For example, the disjuncts in the disjunction (p ∨ q) are p and q.
The truth value of a disjunction is true if and only if the truth value of at least one of its disjuncts is true; otherwise, the truth value is false.
| p |
q |
(p ∧ q) |
| 1 |
1 |
1 |
| 1 |
0 |
1 |
| 0 |
1 |
1 |
| 0 |
0 |
0 |
Note that this is the inclusive or interpretation of the ∨ operator and is differentiated from the exclusive or interpretation in which a disjunction is true if and only if an odd number of its disjuncts are true.
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