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Let A and B be two sets each with a fini...

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.

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Since, there is an injective mapping from A to B, each element of A has unique image in B.
Similarly, there is also an injective mapping from B to A, each element of B has unique image in A or in other words there is one to one onto mapping from A to B.
Thus, there is bijective mapping from A to B.
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