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Logical conjunction

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This page belongs to resource collections on Logic and Inquiry.

Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.

The truth table of \(p ~\operatorname{AND}~ q,\) also written \(p \land q\!\) or \(p \cdot q,\!\) appears below:


\(\text{Logical Conjunction}\!\)
\(p\!\) \(q\!\) \(p \land q\)
\(\operatorname{F}\) \(\operatorname{F}\) \(\operatorname{F}\)
\(\operatorname{F}\) \(\operatorname{T}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{F}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{T}\) \(\operatorname{T}\)


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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.