Please help me prove 2,4, and 5. Thank you
Please help me prove 2,4, and 5. Thank you Theorem 17. Let A, B and C...
help please and thank you 2. Prove that the following statements are true for sets A, B, C: (a) Commutativity (I): An B = BNA. (b) Commutativity (II): AU B = BU A. (c) Distributivity (I): AN(BUC) = (AN B)U(ANC). (d) Distributivity (II): AU (BAC) = (AUB) N (AUC). (e) Idempotence (I): An A = A. (f) Idempotence (II): AU A = A.
A,C,G please 1. Let A, B, and C be subsets of some universal set u. Prove the following statements from Theorem 4.2.6 (a) AUA=/1 and AnA=A. (b) AUO- A and An. (c) AnB C A and ACAUB (d) AU(BUC)= (A U B) U C and An(B n C)-(A n B) n C. (e) AUB=BUA and A n B = B n A. (f) AU(BnC) (AU B) n(AUC) (g) (A U B) = A n B (h) AUA=1( and An-=0. hore...
4. Let A, B, and C be sets. Prove that AU(BNC) = (AUB) n (AUC).
Hi y’all need help with these questions please explain how you solved them thanks . Let A, B, and C be sets (a) Give examples of sets A, B, C such that: (i) AnB-AnC but BC (ii) AUB = AUC but BメC. (b) Now suppose that AnB B = C in this case. AnC and AUB-AUC. Prove that we must have
6. (10 points) Let A, B, and C be sets. Prove (AuB)C(AnC) u(BnC)
#24,28,32 In Exercises 17-40, let (1,2,3, 4,5, 6, 7) 11,3,5,7) U A C (2,3,4, 5,6). Find each of the following sets 17. AnB 20. BU C 23, A,NB, 26. BUC 29. A'U C 32. (AUC)' 35. AnØ 38. BU U 18. ВПС 21. A 24. в'nc 27. (AnC) 30. A' U B' 33. AU0 36. CnØ 39. AnU 19. A U B 22. B' 25. AUC 28. (An B)' 31. (A U B)' 34. CUØ 37. AU U 40. BnU
help please and thank you 5. True or False. For each of the following statements, determine whether the statement is True or False and then prove your assertion. That is, for each True statement provide a proof, and for each False statement provide a counterexample (with explanation). Hint: Draw appropriate Venn diagrams to aid your explorations! Let A, B and C be sets (a) A - (B C) (A - B) C (b) (А — В) — С - (А-С)...
all of these problems please pull in simple terms for problems 5 through 8 let = {1,2,3}, B = {3,4,8}, D = {1,{1}.2 1991 B = {3,4,8}, D = {1,{1},2,{3,2},{@}}, and E = (1.2) 5. AnB = 6. A- E= 7. (ANB) UD= 8. If the universal set is the positive integers, then A= <x< 12}, A = {5,7,9), B = 2.3.4.5). For problems 9-12, let U = {& EZ2 and C = {12, 11,9}. 9. Anc= 10. AU (BNC)...
By only use these axioms to solves the following two questions. Thank you. (AUB)A nB (AnB) AUB 0 EPCA)E P(S)=I PCAUB) P(A) P(B)-PIAne) P(AIB) # ot times A and Boccur #ot times B ocuuts P(ADP(ANB) PCB) P/AB)P(BIA)P(A) P(B) Taew ledr- Using notin The defa P (A I8), The 3 axioms, and T "lews" Teem we have discussed (e. more 1 Show TR P(ALB ) PLACIB) uw-leuti9-2AsSsume AnBUc) (AnB) U (ANC) Mew show Tt Pl(AU B)UC) PIAT+ PCB) Pc) PCANB) PIANC)-...
Please help answer all parts! (1) Prove that 75 is irrational. (State the Lemma that you will need in the proof. You do not need to prove the lemma.) (2) Disprove: The product of any rational number and any irrational number is irrational. (3) Fix the following statement so that it is true and prove it: The product of any rational number and any irrational number is irrational. (4) Prove that there is not a smallest real number greater than...