Exercises for Chapter 17 1. (a) Let A, B be sets. Prove that AUB=A if and...
4. Let A, B, and C be sets. Prove that AU(BNC) = (AUB) n (AUC).
6. (10 points) Let A, B, and C be sets. Prove (AuB)C(AnC) u(BnC)
Please help me prove 2,4, and 5. Thank you Theorem 17. Let A, B and C be sets. Then the following statements are true: (1) AB CA; (2) B CAUB; (3) A CAUB; (4) AB=BA; (5) AU (AUC) = (AUB) UC; (6) An(BNC) = (ANB) nC; (7) An (BUC) = (ANB) U (ANC); (8) AU (BAC) = (AUB) n(AUC).
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.
Let A and B be finite sets. The properties of set operations, prove that: notation denotes the complement. Let the universal set be U. Usin (AUB) n (AUBc) = A
Let A and B be sets. Prove the following statement: B ⊆ A if and only if ¬A ⊆ ¬B
Let A and B be sets. Prove the following statement: B ⊆ A if and only if A ⊆ B.
write the proof problem 3 2. Let A, B and C be sets, then Au(Bnc)-(AUB)n (Auc) 3. Let A and B be sets, then (An B)c-AcUBc.
Prove equalities involving sets A, B, C and D a) (AIB)U(C1B) = (AUC) IB b) (AUB)-(ANB) = (A-8)U(-A) c) (AxB) OLC xD) - (ANC) x (BND) d) (AXB) (BAA) = (ANB)X(AMB)
Let A, B and C be sets. Prove