6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: *...
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...
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).
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.
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.
Let A, B, and be subsets of a universal set U and suppose n(U) - 200, n(A) -21, n(B) = 23, (C) -27, [ AB) - 7, n(ANC) - 10, n(BC) - 13, and ( ABN) - 3. Compute: (a) MAN (BUCI (b) AN (BU09
. Let A, B and C be subset of a universal set U. (a) Prove that: Ac x Bc ⊂ (A × B)c (the universal set for A × B is U × U). So A compliment x B compliment = AxB Compliment
Question 5 16 pts Let set A = {a,b,c} Which of the following are proper subsets of A? {a} a, b {a, b} {a,b,c} {d} Question 6 10 pts Let A = {ne Z | n = 6a + 4 for some integer a} Let B = {me Z m = 18b - 2 for some integer b} Prove or disprove that ASB Hint: follow the method used in Example 6.1.2 on page 338 of the text. HTML Editora B...
Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} be the universal set. Consider the two subsets A = {0, 2, 4, 6, 8} and B = {0,3,6,9}. Use the roster method to write each of the following sets (a) AUB. (b) An B. (c) AC. (d) (AUB) – AC
4·Let A and B be non-empty subsets of a space X. Prove that A U B is disconnected if A n B)U(A nB) 0. Prove that X is connected if and only if for every pair of non-empty subsets A and B of X such that X A U B we have (A B)U (An B)O.