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