Worksheet #4, COMP233 1- Let C (n E n 6r 5 for some integer n and D {m e Z I m 3s 1 for some integer St. Prove or disprove C-D. 2- Let A (1, 3, 5, 7, 9), B 13, 6, 9), and C (2, 4, 6, 8) Find each of the following: b. An B a. AUB c. AUC d. A n Cr h. B n C B-A g. B U C 3- Let Ci fi, -i for all nonnegative integers i. Find a. U o Ci c. Are CO, C1, C2, mutually disjoint? d. U Ci e. n 4- Use an element argument to prove the following statement For all sets A and B, (An B) U (A n BC) A 5- Prove for all sets A and B, (An B) n CA n BC) 6- Prove or disprove for all sets A, B, and C, (An B) u C F An (B u C) 7- Construct an algebraic proof for the given statement. Cite a property from Theorem 6.2.2 for every step. For all sets A, B, and C (A n B) U CE (AUC) n (BUC) For all a and b in B, a b a b. (Hint: Prove that (a b) (a b) 1 and that (a b) (a b) -0, and use the fact that a b has a unique complement