Question

Prove that if f : A → B, g : B → C, and g ◦ f is injective , then f : A injective

Answer 1

Answer:

Check it down.

Step-by-step explanation:

Injective functions or One to one functions are functions in each one element of A set is is mapped to another element of B set

1) Let's start by listing supposition and their respective Reasons

Suppose:

$g\circ f$ is injective then $f:A\rightarrow B$ is also injective.

Reason: Given

2) Since we are dealing with injective (one to one) functions,  we can rightly proceed:

$f(x)=f(y) \:such \:as\: x,y \in A$

$g(f(x))=g(f(y))$

Given the fact that $g\circ f$

$x=y$

Then we can say that since $g\circ f$  f: A is an injective too ("one to one" ) function.