So the interesting thing about this function is that it is a reflexive relation on the set A.

Injective iff. surjective means:

injective surjective and surjective injective.

A function is onto if the range of equals the codomain of .

A function is one-to-one if no member of the codomain is the image under of two distinct elements of the domain.

That is .

if is onto then it follows that but from and is also one-to-one.

And then you have to show it the other way around.

An injective map that is not surjective is .

A surjective map that is not injective is