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# Logical disjunction

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Logical disjunction, also called logical alternation, is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are false.

The truth table of $$p ~\operatorname{OR}~ q,$$ also written $$p \lor q,\!$$ appears below:

 $$p\!$$ $$q\!$$ $$p \lor q$$ $$\operatorname{F}$$ $$\operatorname{F}$$ $$\operatorname{F}$$ $$\operatorname{F}$$ $$\operatorname{T}$$ $$\operatorname{T}$$ $$\operatorname{T}$$ $$\operatorname{F}$$ $$\operatorname{T}$$ $$\operatorname{T}$$ $$\operatorname{T}$$ $$\operatorname{T}$$

## Syllabus

### Logical operators

 Exclusive disjunction Logical conjunction Logical disjunction Logical equality

## Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.