Prove that (A x B) intercepts (C x D) = (A intercepts C) x (B intercepts D)?

Answer 1

Suppose (x,y) is in (AxB)∩(CxD). Then (x,y) is in AxB and (x,y) is in CxD. So x is in A and y is in B and x is in C and y is in D.
So x is in A and C, and y is in B and D.
So x is in (A∩C) and y is in (B∩D).
So (x,y) is in (A∩C) and y is in (B∩D).

Then do the same thing backwards, to show that if (x,y) is in the RHS, (x,y) is in the LHS.

Then you have proven they are equal.

Answer 2

I don't see the question. I am not very good at math.