Prove that if A is a subset of B then A/D is a subset of B/D.
The Attempt at a Solution
Consider element x of A. Since A is a subset of B then for all x element of A, x is an element of B. Consider element x of A/D. If x is an element of D then x is not a member of A and thus it does not matter if x is an element of B. If x is not an element of D and is an element of A than x is also in B because x is an element of A. Thus, A/D is a subset of B.
Not even sure if this much is correct. How do I prove this basic "subtracting a set from both subsets" identity??