- 71

- 0

**[SOLVED] Some Compostion Proofs**

**1. Homework Statement**

Prove:

1.) The composition of subjective functions is subjective

2.) The composition of injective functions is injective

**2. Homework Equations**

Subjective: A function f: A->B is surjective iff

For all members of B, there exists a member of A where f(a)=b

Injective: A funtion f: A->B in injective iff

f(a)=f(b) -> a=b

**3. The Attempt at a Solution**

I really don't know how to start this proof, mainly because in the questions, the domain and codomain are not defined in any way. However, both statements seem to be obviously true to me, at least I can't think of any obvioius counter examples.

I.) Suppose we have functions f an g which are both surjective. The conpostion of these functions can b e written as g(f(x)). If g is subjective, regardless of the values of f(x), then gof will be subjective.

That proof's really bad I know, and I don't know how to even start 2. Help! It seems like it should be really easy and I feel like an idiot for not knowing how to do these proofs.