A,C,G please 1. Let A, B, and C be subsets of some universal set u. Prove...
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).
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)
Let A, B, C be subsets of a universal set U. Recall for D C U that XD denotes the characteristic function of D. Prove that XAUBUC = XA + XB+XC - XACB - XAC - XB C +XAOBOC. Hint: Facts that you may use: (1) XD 1-XD. (2) (AU BUC)° = ACB 1C. (3) XEnF = XEXF. (4) XEnFnG = XEXFXG. Don't prove these facts.
5. Let A, B, C be subsets of a universal set U. Recall for D CU that XD denotes the characteristic function of D. Prove that XAUBUC = XA +XB+XC - XAMB - XAOC · XBNC + XANBNC. Hint: Facts that you may use: (1) Xpe = 1 – Xd. (2) (AU BUC)° = A n Bºn Cº. (3) XEnF = XEXF. (4) XEnFnG XEXFXG. Don't prove these facts.
D Question 7 Let A and B be subsets of a universal set U with n (U)-32, n (A) = 11, n (B) = 17, and n (AUB) = 25. Compute n(A' nB) D Question 8 Let A and B be subsets of a universal set U with n (U)-32, n (A)-11, n (B)-17, and n (A U B)=25 Compute n (AUB).
(e) For subsets {A,Jael, prove that2 I) Evaluate (g) Prove that XAAB (XA-X) (h) Use characteristic functions to prove the distributive law: AU(BnC) (AUB)n (AUC) Hint: start with the right-hand side. 1In this problem, the product of two functions and g is defined by (Jg)(x)-f() and the sum is defined by (f +g)(x) :-f(x) + g(x), as usua 2Here, Π denotes the product of an indexed set of numbers. For example: rL TL TL i n! i-1 -1 (e) For...
8. Let A and B be subsets of some universal set U. From Proposition 5.10, we know that if A S B, then B S A. Now prove the following proposition: For all sets A and B that are subsets of some universal set U, A C B if and only if B S A.
someone please help Let U be the universal set, where: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17) Let sets A, B, and C be subsets of U, where: A = {1, 3, 4, 5, 12, 14, 15) B = {1, 2, 7, 13} C = {3, 7, 10, 14, 16} Find the following: LIST the elements in the set A U : AU = { Enter the elements...
4. Let A, B, and C be sets. Prove that AU(BNC) = (AUB) n (AUC).
Let A, B, C be subsets of U. Prove that If C – B=0 then AN (BUC) < ((A-C)) UB