Editing Logical equivalence (section)

{{Short description|Concept in logic}}
In [[logic]] and [[mathematics]], statements <math>p</math> and <math>q</math> are said to be '''logically equivalent''' if they have the same [[truth value]] in every [[model (logic)|model]].<ref>{{Cite book|title=Introduction to Mathematical Logic|url=https://archive.org/details/introductiontoma00mend|url-access=limited|last=Mendelson|first=Elliott|authorlink = Elliott Mendelson|year=1979|edition=2|pages=[https://archive.org/details/introductiontoma00mend/page/n63 56]|publisher=Van Nostrand |isbn=9780442253073}}</ref> The logical equivalence of <math>p</math> and <math>q</math> is sometimes expressed as <math>p \equiv q</math>, <math>p :: q</math>, <math>\textsf{E}pq</math>, or <math>p \iff q</math>, 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.