Loterre: Mathematics: logical equivalence

mathematical logic > logical equivalence

logical equivalence

In logic and mathematics, statements ${\\displaystyle p}$ and ${\\displaystyle q}$ are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of ${\\displaystyle p}$ and ${\\displaystyle q}$ is sometimes expressed as ${\\displaystyle p\\equiv q}$ , ${\\displaystyle p::q}$ , ${\\displaystyle {\ extsf {E}}pq}$ , or ${\\displaystyle p\\iff q}$ , 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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Logical_equivalence)