Theorem 3.8: If

is a one to one correspondence, then

f -1f = iA and ff -1 = iB

Proof: Let a be an element of A. Let b = f (a ). Then

f -1f(a) = f -1(b) = a

by Definition 3.10, the definition of the inverse function.

Let b be an element of B. Let a = f-1(b). Then

ff-1(b) = f(a) = b

by Definition 3.10, the definition of the inverse function.