Determine the sets A and B 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} Prove that: A▲B. (4m) jun 2014 Solution: A▲B-A) U (A-B). Let A=P1 U P2 B=P2 U P3 A▲B = (AUB)-(A∩B) = (P1 U P2 UP3) (P2) = P1 U P3 (1) – ………… B A = P3, A B = P1 – – Therefore (B A) U (A B) = P3 U P1……………………… (2) – – A=U - A = P3 U P4, AND B=U B = P1U P4 – B A= P3, A B = P1 Therefore (B A1) U (A B1) = P3 U P1…………………… ∩ ∩ ∩ ∩ (3) From (1), (2) and (3), A▲B= (B∩A) U (A∩B) = (B-A) U (A-B). 14. Using Venn diagram, prove the following property of the symmetric difference: A (B▲C) = (A▲B) C (4m) jan 2015 ▲ ▲ Solution: By using Venn diagram,
Determine the sets A and B 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 Prove that: A▲B. (4m) jun 2014 Solution: A▲B-A) U (A-B). Let A=P1 U P2 B=P2 U P3 A▲B = (AUB)-(A∩B) = (P1 U P2 UP3) – (P2) = P1 U P3 ………… (1) B – A = P3, A – B = P1 Therefore (B – A) U (A – B) = P3 U P1……………………… (2) A=U - A = P3 U P4, AND B=U – B = P1U P4 B ∩ A= P3, A ∩ B = P1 Therefore (B ∩ A1) U (A ∩ B1) = P3 U P1…………………… (3) From (1), (2) and (3), A▲B= (B∩A) U (A∩B) = (B-A) U (A-B). 14. Using Venn diagram, prove the following property of the symmetric difference: A ▲ (B▲C) = (A▲B) ▲ C (4m) jan 2015 Solution: By using Venn diagram,
Unit-I-II-solutions.docx