# Converse (logic)

reverse of a categorical or hypothetical proposition

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

## References

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.