Logical equivalence

In logic, statements p {displaystyle p} and q {displaystyle q} are logically equivalent if they have the same logical content. That is, if they have the same truth value in every model (Mendelson 1979:56). The logical equivalence of p {displaystyle p} and q {displaystyle q} is sometimes expressed as p ≡ q {displaystyle pequiv q} , E p q {displaystyle { extsf {E}}pq} , or p ⟺ q {displaystyle piff q} .However, these symbols are also used for material equivalence. Proper interpretation depends on the context. Logical equivalence is different from material equivalence, although the two concepts are closely related. In logic, statements p {displaystyle p} and q {displaystyle q} are logically equivalent if they have the same logical content. That is, if they have the same truth value in every model (Mendelson 1979:56). The logical equivalence of p {displaystyle p} and q {displaystyle q} is sometimes expressed as p ≡ q {displaystyle pequiv q} , E p q {displaystyle { extsf {E}}pq} , or p ⟺ q {displaystyle piff q} .However, these symbols are also used for material equivalence. Proper interpretation depends on the context. Logical equivalence is different from material equivalence, although the two concepts are closely related. Logical equivalences involving conditional statements： Logical equivalences involving biconditionals：