Pronunciation: /ˌɪm.plɪˈkeɪ.ʃən/ Explain

An implication is an "If then" statement:

If antecedent then consequent.
If P implies Q, then if P is true, Q must be true, and if P is false, Q must be false. An implication is written PQ. In this example P is the antecedent and Q is the consequent.


If the sides of a rectangle are congruent, then the rectangle is also a square. The antecedent is 'the sides of a rectangle are congruent'. The consequent is 'the rectangle is also a square'.


  1. McAdams, David E.. All Math Words Dictionary, implication. 2nd Classroom edition 20150108-4799968. pg 94. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Implication. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

4/23/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/6/2018: Initial version. (McAdams, David E.)

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