# Logical equivalence

## Concept in logic / From Wikipedia, the free encyclopedia

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In logic and mathematics, statements $p$ and $q$ are said to be **logically equivalent** if they have the same truth value in every model.^{[1]} The logical equivalence of $p$ and $q$ is sometimes expressed as $p\equiv q$, $p::q$, ${\textsf {E}}pq$, or $p\iff q$, depending on the notation being used.
However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related.