I am somewhat confused by your post.
Is this a solution to (j)? First, , not . I also don't see how the second line follows from the first or vice versa. And the last line:B - C = BnC^complement <= A^complement
AnB = (AnB)^complement => C^complment
is it what one needs to prove?A^complement <= BnCcomplement
Then, if the typesetting was not messed up, you are talking about the set difference , which I don't see in any problem (in fact, set difference in the picture is denoted differently).