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Logical equivalence
Concept in logic
In logic and mathematics, statements p {\displaystyle p} and q {\displaystyle q} are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p ⟺ q {\displaystyle p\iff q} , depending on the notation being used.
From Wikipedia
In logic and mathematics, statements p {\displaystyle p} and q {\displaystyle q} are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p ⟺ q {\displaystyle 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.
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