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Concept
Logical equivalence
Summary
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. 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.
Logical equivalences
In logic, many common logical equivalences exist and are often listed as laws or properties. The following tables illustrate some of these.
General logical equivalences
Logical equivalences involving conditional statements
:#p \implies q \equiv \neg p \vee q
:#p \implies q \equiv \neg q \implies \neg p
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Official source
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