If f is a one-to-one function from X to Y and g is a one-to-one function from Y to Z, you prove that g ∘ f is one-to-one by supposing that _____and then showing that______.

To fill:

If f is a one-to-one function from X to Y and g is a one-to-one function from Y to Z, you prove that g∘f is one-to-one by supposing that _____ and then showing that _____.

Given information:

The given statement is,

“A one-to-one correspondence from a set X to a set Y is a _______ that is _________”.

Since, f:X→Y such that

f(x)=y

And

g:Y→Z such that

g(y)=z

Then, (g∘f)(x1)=(g∘f)(x2)g(f( x 1 ))=g(f( x 2