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Get Answers to all your Questions
7.(vi) Refer to question 6 above, state true or false: (give reason for your answer)
(vi) are mutually exclusive and exhaustive.
Answers (1)
Here,
S = {(x,y): 1 x,y
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)}
C = {(1, 1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1)}
(vi) X and Y are mutually exclusive if and only if X Y =
A'
B' = B
A =
(from (iii) and (i))
Hence A' and B' are mutually exclusive.
Again,
B'
C = A
C
(from (iv))
Hence B' and C are not mutually exclusive.
Hence, A', B' and C are not mutually exclusive and exhaustive. FALSE
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