Question

Let f: X->Y be a function mapping the set X to the set Y
Let A,B be subsets of the set X, and C,D be subsets of the Set Y
Prove f(A intersect B) is a proper subset of f(A) intersect f(B)

I'm having some conceptual difficulty on even starting this.

I've tried going the route of assume x is an element of A intersect B, which implies x is an element of A and x is an element of B. But as far as what to do next I'm stuck.

Answer 1

@robkee This is a bit out of my domain of knowledge, the most I could suggest for helping you visualize this is to do what I'd: make some Venn-diagrams :-D