Solution: (A-B) C = (A∩B) – ∩C = A∩ (B∩C) = A∩ (B∩C) = A (B∩C) – (A C) (B C) = (A (B C) – – – –C) ∩ – = (A C) (B C1) ∩ ∩ – = (A C) (BU C) ∩ ∩ = [(A C) B)] U [(A C) ∩ ∩ ∩ ∩C] = [(A (C∩B)] U [A (C∩C)] ∩ ∩ = [A (CUB) ] U (A∩Ø) ∩ = [A (BUC) ] UØ ∩ = [A (BUC) ] ∩ = [A - (BUC)] (8m) jun 2014 11. Explain the laws of set theory: Determine the sets A and B given that A B = {1, 3, 7, 11}, B A = {2, 6, – – 8} and A∩B = {4, 9} (5m) jun 2014 Solution: set A = (A B) + (A∩B) – = [{1, 3, 7, 11}] + [{4, 9}] = {1, 3, 4, 7, 9, 11} Set B = (B-A) + (A∩B) = [{2, 6, 8}] [{4, 9}] – = {2, 4, 6, 8, 9} that: A▲B. (4m) jun 2014 Solution: A▲B-A) U (A-B). Let A=P1 U P2 B=P2 U P3
Solution: (A-B) – C = (A∩B) ∩C = A∩ (B∩C) = A∩ (B∩C) = A – (B∩C) (A – C) – (B – C) = (A –C) ∩ (B – C) = (A ∩ C) ∩ (B – C1) = (A ∩ C) ∩ (BU C) = [(A ∩ C) ∩ B)] U [(A ∩ C) ∩C] = [(A ∩ (C∩B)] U [A ∩ (C∩C)] = [A ∩ (CUB) ] U (A∩Ø) = [A ∩ (BUC) ] UØ = [A ∩ (BUC) ] = [A - (BUC)] 11. Explain the laws of set theory: (8m) jun 2014 Determine the sets A and B given that A – B = {1, 3, 7, 11}, B – A = {2, 6, 8} and A∩B = {4, 9} Solution: set A = (A – B) + (A∩B) = [{1, 3, 7, 11}] + [{4, 9}] = {1, 3, 4, 7, 9, 11} Set B = (B-A) + (A∩B) = [{2, 6, 8}] – [{4, 9}] = {2, 4, 6, 8, 9} (5m) jun 2014 that: A▲B. (4m) jun 2014 Solution: A▲B-A) U (A-B). Let A=P1 U P2 B=P2 U P3
DMS-QUESTIONS-WITH-SOLUTION.docx