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# State/Bijections are injective and surjective functions

Proposition: (Bijections are injective and surjective functions) Suppose that $X$ and $Y$ are sets, and $f \colon X \rightarrow Y$ is a function. Then $f$ is a bijection if and only if $f$ is both injective and surjective.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Bijection, Def/Injective, Def/Surjective, State/Injective functions have left inverses, State/Surjective functions have right inverses, Def/Composite function

The following statements and definitions rely on the material of this page: State/Composing injective surjective or bijective functions yields the same

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