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

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

(ii) A and B are mutually exclusive and exhaustive

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Here,

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)}

(ii) X and Y are mutually exclusive if and only if X $\cap$ Y = $\phi$

$\cap$ B = $\phi$ , since A and B have no common element amongst them.

Hence, A and B are mutually exclusive.

Also,

$\cup$ B = {(2,1), (2,2).... (2,6), (4,1), (4,2).....(4,6), (6,1), (6,2)..... (6,6), (1,1), (1,2).... (1,6), (3,1), (3,2)..... (3,6), (5,1), (5,2).... (5,6)} = S

Hence, A and B are exhaustive.

TRUE

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