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## Homework Statement

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)

## 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!