# What is the difference between “logical equivalence” and “material equivalence”?

Wikipedia offers this as the difference between "logical equivalence" and "material equivalence":

Logical equivalence is different from material equivalence. Formulas p and q are logically equivalent if and only if the statement of their material equivalence (P ⟺ Q) is a tautology.

Material equivalence is associated with the biconditional. However, I am still unclear what the difference is between the two.

I want to make sure I am using the terms correctly. Recently to avoid confusion I dropped the adjective "logically" in front of the following use of "equivalent":

Using De Morgan's laws, ¬(A ∧ ¬B) is equivalent to ¬A ∨ B.

If there is any difference between the two terms, what is it? Perhaps an example of the correct use of each would help clarify the difference.

If there isn't any difference I probably shouldn't use either one.

Wikipedia contributors. (2019, February 13). Logical equivalence. In Wikipedia, The Free Encyclopedia. Retrieved 11:22, August 3, 2019, from https://en.wikipedia.org/w/index.php?title=Logical_equivalence&oldid=883191333