---
tag: 0RVYE75E2M
kind: definition
name: Converse
msc: [03B05]
defines: 09A3N7ZN5G
uses: [0ZNX6DQ3EJ]
sources:
  - url: https://en.wikipedia.org/wiki/Converse_(logic)
    locator: lead section
---

## Definition

Let $p$ and $q$ be [[propositions|0ZGC7ZESYN]].
The converse of the [[implication|0ZNX6DQ3EJ]] $p \to q$ is the implication $q \to p$.

## Remarks

An implication and its converse are not [[logically equivalent|06GYGS41JK]].
For example, "if $n = 2$, then $n$ is prime" is true, but its converse "if $n$ is prime, then $n = 2$" is false.
The inverse of $p \to q$ is $\neg p \to \neg q$. It is the [[contrapositive|04T1CT7212]] of the converse.

## Explanations

### L1 human

The converse reads the arrow backwards.
"If an animal is a dog, then it is a mammal" is true.
Its converse, "if an animal is a mammal, then it is a dog", is false.