Prove Theorem 7.3.1(b): If f is any function from a set X to a set Y, then I Y ∘ f = f , where I Y is the identity function on Y.

To Prove:

IY∘f=f, for any function f from a set X to a set Y, where IY is the identity function on Y.

Given information:

f is a function from a set X to a set Y, and IY is the identity function on Y .Concept used:

fog(x)=f(g(x)).

Proof:

Suppose f is a function from a set X to a set Y and IY is the identify function on Y.

Then for all x in X,

(IY∘f)(x)=IY(f(x))                  =IY(