Injectivity and Surjectivity in Function Compositions

[tomboi03]

Let f: A->B and g: B->C
a. C₀$$\subset$$C, show that (g o f)^-1(C₀))=f^-1(g^-1(C₀)).
b. If f and g are injective, show that g o f is injective
c. If g o f is injective, what can you say abuot injectivity of f and g?
d. If f and g are surjective, show that g o f is surjective.
e. If g o f is surjective, what can you say about surjectivity of f and g.
f. Summarize your answers to (b)-(e) in the form of a theorem

I don't know how to do this... can someone else me..?

Thank You

 

[tiny-tim]

Hi tomboi03!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

Start with part a. … take a typical member of the LHS, and prove that it is in the RHS … then do it the other way round.