Logical Equivalence

Pronunciation: /ˈlɑdʒ.ɪ.kəɫ ɪˈkwɪ.və.ləns/ Explain

Two statments are logically equivalent if, for all cases, if one is true then the other is true, and if one is false then the other is false. Logical equivalence is used in proofs.

Examples:

In each of these examples, P represents a logical statement.

• P and TRUE ≡ P
• P and FALSE ≡ False
• P or P ≡ P
• NOT NOT P ≡ P

Cite this article as:

McAdams, David E. Logical Equivalence. 4/24/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/l/logicalequivalence.html.

Revision History

4/24/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/31/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/30/2018: Initial version. (McAdams, David E.)