Question

show that if a is A subset of B then C minus B subset of C minus A

Answer 1

Note that x in A ==> x in B is equivalent to its contrapositive

x not in B ==> x not in A.

(1) If x is in C - B, then x is in C and x is not in B.

By the above note, this means that x is in C and x is not in A.

Hence x is in C - A.

(2) The converse is false.

Let C = {1}, A = {1,2}, B = {1}.

So, C - B = C - A are both empty sets (hence C - B is a subset of C - A), but A is not a subset of B.

I hope that helps!