Converse (logic)

In mathematics and logic, a converse is a variant of an implication. More specifically, given an implication of the form [math]\displaystyle{ P \to Q }[/math], the converse is the statement [math]\displaystyle{ Q \to P }[/math]. [1]

While a converse is similar to its originating implication, they are not logically equivalent.[2] This means that the truth of an implication does not guarantee the truth of its converse (and vice versa).[1]

As a logical connective, the converse of [math]\displaystyle{ P }[/math] and [math]\displaystyle{ Q }[/math] can be represented by the symbol [math]\displaystyle{ \leftarrow }[/math] (as in [math]\displaystyle{ P \leftarrow Q }[/math]).[3]

Converse (logic) Media

Related pages

References

  1. 1.0 1.1 "The Definitive Glossary of Higher Mathematical Jargon". Math Vault. 2019-08-01. Retrieved 2020-10-09.
  2. Taylor, Courtney. "What Are the Converse, Contrapositive, and Inverse?". ThoughtCo. Retrieved 2020-10-09.
  3. "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-10-09.