(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.