# Proof-injection,bijection

• Jan 17th 2008, 03:12 PM
anncar
Proof-injection,bijection
f: X--->Y and g: Y----> Z are functions. Prove that

a) if both f and g are injective then g*f is injective

b) if both f and g are surjective then g*f is surjective

c) if both g*f is a bijection, then f is an injection and g is a surjection

( * is that small circle that means one function 'plugged into' into another)
• Jan 17th 2008, 03:30 PM
Jhevon
Quote:

Originally Posted by anncar
f: X--->Y and g: Y----> Z are functions. Prove that

a) if both f and g are injective then g*f is injective

b) if both f and g are surjective then g*f is surjective

c) if both g*f is a bijection, then f is an injection and g is a surjection

( * is that small circle that means one function 'plugged into' into another)

similar problems were dealt with here. see if it helps. if it doesn't come back. i hope you know the defintions of injective, surjective and bijective before even thinking about proceeding with these questions. the first 2 or 3 posts and the last post is relevant. in the middle, there's a lot of philosophical stuff