Question

A and B are two non empty sets. . . Every function from A to B is one one ..then A must be a singleton set. .prove it?

Answer 1

Step-by-step explanation:

A and B are two non-empty sets.

Let f be a function from A→B.

It is given that there is an injective map from A→B.

⇒ That means f is one-one function.

It is also given that there is an injective map from B→A.

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

⇒ f is onto function or surjective.

If a function is both injective and surjective, then the function is bijective.

∴ f is bijective.