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Refer to question 6 above, state true or false: (give reason for your answer) (vi) A′, B′, C are mutually exclusive and exhaustive.

7.(vi)     Refer to question 6 above, state true or false: (give reason for your answer)

             (vi) {A}',{B}',C are mutually exclusive and exhaustive.

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Here,

S = {(x,y): 1 \leq x,y \leq 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 \cap Y = \phi

\therefore A' \cap B' = B \cap A = \phi (from (iii) and (i))

Hence A' and B' are mutually exclusive.

Again,

\therefore B' \cap C = A \cap C \neq \phi (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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