Problem #33, page 258

(1) FIRST: I see that in some copies of the text, there is a misprint of the statement of this problem. The correct version of the problem is: For all sets A,B, and C, (A-B)+(B-C) = (A+B)-(B.C) (2) SECOND: The proof boils down to showing that: A-C is a subset of (A-B) + (B-C) One way to prove this is to first prove that: A-C = [A-(B+C)] + [(A.B)-C] Then prove that: A-(B+C) is a subset of A-B and that (A.B)-C is a subset of B-C (3) THIRD: Please note that "+" denotes UNION, and "." denotes INTERSECTION.