Editing Logical equivalence (section)

==Relation to material equivalence==

Logical equivalence is different from material equivalence. Formulas <math>p</math> and <math>q</math> are logically equivalent if and only if the statement of their material equivalence (<math>p \leftrightarrow q</math>)  is a tautology.<ref>{{Cite book|title=Introduction to Logic|last1=Copi|first1=Irving|author1link = Irving Copi|last2=Cohen|first2=Carl|author2link = Carl Cohen (philosopher)|last3=McMahon|first3=Kenneth|publisher=Pearson|year=2014|edition=New International|pages=348}}</ref>

The material equivalence of <math>p</math> and <math>q</math> (often written as <math>p \leftrightarrow q</math>) is itself another statement in the same [[formal system|object language]] as <math>p</math> and <math>q</math>. This statement expresses the idea "'<math>p</math> if and only if <math>q</math>'". In particular, the truth value of <math>p \leftrightarrow q</math> can change from one model to another.

On the other hand, the claim that two formulas are logically equivalent is a statement in [[metalanguage]], which expresses a relationship between two statements <math>p</math> and <math>q</math>. The statements are logically equivalent if, in every model, they have the same truth value.