# Ex 16.2, 7

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) • A and B are mutually exclusive From 16.2 ,6 A = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 B = 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6 A ∩ B = ϕ Since no common element in A & B So, A & B are mutually exclusive True. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (ii) A and B are mutually exclusive and exhaustive From 16.2 ,6 A = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 B = 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6 A ∪ B = 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6,= S Since A ∪ B = S They are exhaustive events Also as per (i), they are mutually exclusive Hence they are mutually exclusive and exhaustive True. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (iii) A = B’ A = getting even number on the first A = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 B = getting odd no on the first die = 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6 B’ = getting even number on the first die = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 = A Hence A = B’ True. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (iv) A and C are mutually exclusive A = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 C = (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1) A ∩ C = { 3, 6, 4, 5, 5, 4, 6, 3, 6, 6} ≠ 𝜙 Since there is common elements in A and C , So A & C are not mutually exclusive False. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (v) A and B’ are mutually exclusive A = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 B’ = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 A ∩ B’ = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 = A Since A ∩ B’ = A ≠ ϕ Hence there is common element between A & B’ Hence A and B’ is not mutually exclusive Hence, false Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (vi) A,’ B’, C are mutually exclusive and exhaustive. A = getting an even number on the first die A’ = getting an odd number on the first die A’ = 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6 B = getting an odd number on the first die B’ = getting an even number on the first die B’ = 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6 6 & C = (1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1) A’ ∩ B’ = 𝝓 Hence there is no common element in A’ and B’ A & B are mutually exclusive B’ ∩ C = { 2, 1, 2, 2, 2, 3, 4, 1} Hence there is common element between B’ and C Since B’ ∩ C ≠ 𝜙 Hence B’ and C are not mutually exclusive Since B’ & C are not mutually exclusive A,’ B’, C are not mutually exclusive and exhaustive ∴ A,’ B’, C are not mutually exclusive and exhaustive Hence, false

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.