   Chapter 1.3, Problem 11E

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# Let g : A → B and f : B → C . Prove that g is one-to-one if f ∘ g is one-to-one.

To determine

To prove: The function g is one-to-one function if fg is one-to-one.

Explanation

Given Information:

The function g:AB, the function f:BC.

Proof:

Let us assume that fg is one-to-one.

Now, we will prove that g is one-one.

Let a,bA such that g(a)=g(b). Since, f is a function, this equality gives,

f(g(a))=f(g(b))(fg)(a)

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