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
Venn diagram of P \leftarrow Q The white area shows where the statement is false.
- Venn
- Venn
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Converse of a simple mathematical relation
Related pages
References
- ↑ 1.0 1.1 The Definitive Glossary of Higher Mathematical Jargon (in en-US). Math Vault (2019-08-01). Retrieved 2020-10-09.
- ↑ Taylor, Courtney. What Are the Converse, Contrapositive, and Inverse? (in en). ThoughtCo. Retrieved 2020-10-09.
- ↑ Comprehensive List of Logic Symbols (in en-US). Math Vault (2020-04-06). Retrieved 2020-10-09.