# Injective functions

1. Nov 2, 2009

### XodoX

1. The problem statement, all variables and given/known data
Mark as true or false.
(a) A function is injective if a 6$$\neq$$ b yields f(a) 6$$\neq$$ f(b).
(b) A function is injective if f(a) = f(b) in case that a = b.
(c) A function is injective if f(a) = f(b) only if a = b.
(d) A function is injective only when f(a) 6$$\neq$$ f(b) yields a 6$$\neq$$ b.

3. The attempt at a solution

a) False
b) True
c) True
d) True

I know that f is said to be injective, if and only if f(a) = f(b) implies that a = b.

1. The problem statement, all variables and given/known data

Mark as true or false. If f : E ! E is a map on a finite set then
(a) If f is injective then f is surjective.
(b) If f is surjective then f is injective.
(c) There is an injective map f from the set of natural numbers N to itself which is not surjective.
(d) There is a surjective map f from the set of natural numbers N to itself which is not injective.

I don't really get this. Probably easy, but badly explained in the book. Can someone clarifiy this one for me, please?

Thank you

Last edited: Nov 2, 2009