61. Prove or sets A, B, and C disprove: A A (BnC) (A A B) n (A A C) for all
Problem 2. Let A, B be sets. Prove that if ACB, then P(A) CP(B). Explain why we can conclude that if A= B, then P(A) = P(B). Problem 3. Let A.B be sets. Prove that if P(A) CP(B), then ACB. Explain why we can conclude that if P(A) = P(B), then A= B.
Prove or disprove: for all sets A, B, C and D, (Ax B) U (Cx D) (AUC) x (BUD).
Exercise 2. Prove or disprove the following: a) C € P(A) + CCA b) ACB + P(A) CP(B) c) A=0 + P(A) = 0
(1) Prove or disprove the following statements. (a) Let a, b and c be integers. If aſc and b|c, then (a + b)|c (b) Let a, b and c be integers. If aſb, then (ac)(bc)
This is a discrete math question: Exercise 5. Let A and B be sets. Prove or disprove: AAB| = |A - B+B - AL. Claim. Proof
Questions: 1. Let P be the statement: "For all sets A, B and C. if AUB CAUC then B - ACC." (a) Is P true? Prove your answer. (b) Write out the converse of P. Is the converse of P true? Prove your answer. (c) Write out the contrapositive of P. Is the contrapositive of true? Explain.
discrete math question using proofs to determine to prove the following equation or disprove it 4. Prove or disprove. Let A, B, C, and D be sets. Then (Ax B)n (CxD) (Ancx (B nD) 5. Prove or disprove: {2k 1 k E Q} {4" | k E Q) F6 7 Prove or disprove. Let A be a set and let I be an arbitrary index set for a collection of sets {Be l α E 1). Then, 6. An(UP)-a αΕΙ
Let A, B and C be sets. Prove
6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A) 6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A)