Logical equivalence: Difference between revisions
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In [[logic]], statements ''p'' and ''q'' are '''logically equivalent''' if they have the same logical content. |
In [[logic]], statements ''p'' and ''q'' are '''logically equivalent''' if they have the same logical content. |
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Revision as of 12:54, 27 September 2005
- See also Logical biconditional.
In logic, statements p and q are logically equivalent if they have the same logical content.
Syntactically, p and q are equivalent if each can be proved from the other. Semantically, p and q are equivalent if they have the same truth value in every model.
Logical equivalence is often confused with material equivalence. The former is a statement in the metalanguage, claiming something about statements p and q in the object language. But the material equivalence of p and q (often written "p ↔ q") is itself another statement in the object language. There is a relationship, however; p and q are syntactically equivalent if and only if p ↔ q is a theorem, while p and q are semantically equivalent if and only if p ↔ q is a tautology.
Logical equivalence is sometimes denoted p ≡ q or p ⇔ q. However, the latter notation is also used for material equivalence.