Let A and B be two sets each with a finite number of elements. Assume that there is an injective mapping from A to Band that there is an injective mapping from B to A Prove that there is a bijective mapping from A to B.

Explanation

A and `B` are two non empty sets.


Let `f` be a function from `A` to `B`.


It is given that there is injective map from `A` to `B`.


That means `f` is one-one function .


It is also given that there is injective map from `B` to `A`.


That means every element of set `B` has its image in set `A`.


`Rightarrow {f}` is onto function or surjective.


`therefore f` is bijective.


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