Let A B and C each be sets in the universe U Directly prove

Let A, B, and C each be sets in the universe U. Directly prove that (A - C) times (B - C) subsetofequalto (A times B) - (C times C). Explain how you know (A - C) times (B - C) notequalto (A times B) - (C times C).

Solution

(A-B) IS THE SET OF ELEMENT that are in A but not in B

(B-C) is the set of elements in B but not in C

(A-C)*(B-C) IS THE SET OF ELEMENTS THAT are in elements of (A*B) and (B*C)

THEREFORE ,it is proved