3. For any three sets A, B, C A - (BUC)
Answers
12. Let A, B, and C be any three sets. Prove that (a) A-B AnB (c) A-(B-C) An(BUC) (b) A (A-B) U (A n B) (d) (A - B)-C-A-(BUc) 13. Comment on the following statements. Are they syntactically correct? 14. Prove or disprove each of the following statements about arbitrary sets A and B. If you think a statement is true, prove it; if you think it is false, provide a counterexample. (a) p(AnB) (A) p(B) (b) p(AUB) (A) Uo(B) (c) p(4 - B) (A) (B) Remark. To show that two sets U and V are equal, we usually want to prove that r e Ure V. In this problem, the element r is actually a set. Since we usually use uppercase letters to denote sets, we should start the proof of (a) with "Let S Ep(AnB If you prefer to use the alternate approach, it looks like the following: )." SEP(A)np(B)