Given A and B are two finite sets. There are injective maps from both A to B and B to A.

Let f be the injective map defined from A to B.

Thus, we have f is one-one.

We also know that there is a one-one mapping from B to A.

This means that each element of B is mapped to a distinct element of A.

But, B is the co-domain of f and A is the domain of f.

So, every element of the co-domain of the function f has a pre-image in the domain of the function f.

Thus, f is also onto.

Therefore, f is a bijection as it is both one-one and onto.

Hence, there exists a bijection defined from A to B.