Converse, inverse, contrapositive

Definitions.
- Converse: $Q\Rightarrow P$.
- Inverse: $\neg P\Rightarrow\neg Q$.
- Contrapositive: $\neg Q\Rightarrow\neg P$.

Equivalence. $P\Rightarrow Q$ is equivalent to its contrapositive $\neg Q\Rightarrow\neg P$. Converse and inverse are equivalent to each other but not to the original.

Example. $P\Rightarrow Q$: "if $n$ even then $n^2$ even". Contrapositive: "if $n^2$ odd then $n$ odd". Converse: "if $n^2$ even then $n$ even" (true here, but not always).

Conclusion. Contrapositive is logically equivalent to the implication.