Converse (logic)

In mathematics and logic, a converse is a variant of an implication. More specifically, given an implication of the form $P\to Q$ , the converse is the statement $Q\to P$ . ^[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 $P$ and $Q$ can be represented by the symbol $\leftarrow$ (as in $P\leftarrow Q$ ).^[3]

Related pages

Contrapositive

References

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

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[:0-1] 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.

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