logical equivalence

Two formula are logically equivalent if they share the same truth value for all truth assignment.

Not to be confused with equivalence relation and logical biconditional

Common Logical Equivalences

Equivalence	Name
	Identity Law
	Domination laws
	Idempotent or tautology laws
	Double Negation
	Commutative laws
	Associative laws
	Distributive laws
	De Morgan’s laws
	Absorption laws
	Negation laws
	Law of Contraposition
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Relationship with Biconditional

See: logical biconditional

and are logical equivalent if and only if when the biconditional is always true (a tautology).

Substitutability

In propositional logic, if a proposition is logically equivalent to a propositional , then we can substitute for and the result will be logically equivalent to the original sentence. However, this is no longer true in predicate logic.

Footnotes

1. Logical equivalence - Wikipedia ↩