(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f: X -> Y is a map from X to Y. And A, B subset X are random subsets of X. Proof the following:

a) if A subset B then f(A) subset f(B)

3. The attempt at a solution

(1)Take an arbitrary element x in f(A).

(2)For every x there has to be a y in A so that f(y)=x

(3)From A subset B: for every y in A, y in B

(4)So for every x in f(A) there has to be a y in f(B)

(5)So f(A) subset f(B)

I'm terrible at this, I came up with this proof but I'm wondering if my reasoning from step 3 to 4 is correct. Can someone help me?

Thanx in advance!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Set Theory| Proof if A subset B then f(A) subset f(B)

**Physics Forums | Science Articles, Homework Help, Discussion**