1. The problem statement, all variables and given/known data A,B,C,D are sets. Prove that if C is contained in A and D is contained in B, then C∩ D is contained in A∩ B. 2. Relevant equations 3. The attempt at a solution Let x be any element. Then There exists (x that belongs to C∩D) and (x does not belong to A∩ B) So x belongs to C and x belongs to D If x belongs to C, since C is contained in A, then x belongs to A. If x belongs to D, since D is contained in B, then x belongs to B. So x belongs to A intersect B, a contradiction. Then the original statement is true. Is it okay?