Logical equality

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This page belongs to resource collections on Logic and Inquiry.

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

The truth table of \(p ~\operatorname{EQ}~ q,\) also written \(p = q,\!\) \(p \Leftrightarrow q,\!\) or \(p \equiv q,\!\) appears below:

\(\text{Logical Equality}\!\)
\(p\!\) \(q\!\) \(p = q\!\)
\(\operatorname{F}\) \(\operatorname{F}\) \(\operatorname{T}\)
\(\operatorname{F}\) \(\operatorname{T}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{F}\) \(\operatorname{F}\)
\(\operatorname{T}\) \(\operatorname{T}\) \(\operatorname{T}\)


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