Set relations and set operations

Question

Prove using logical equivalences and valid argument forms.

Let U be the Universal set and A,B a subset of U

If A is a subset of B and X is not an element of B, then X is not an element of A

Answer 1

Suppose that X is an element of A. Then, since A is a subset of B we have that X must be an element of the set B too. But this is a contradiction since by assumption X is not an element of B. The proof is complete.