# 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.

H Harsh Kankaria

Here,

S = {(x,y): 1 $\dpi{80} \leq$ x,y $\dpi{80} \leq$ 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 = $\phi$

$\dpi{100} \therefore$ A' $\cap$ B' = B $\cap$ A = $\phi$ (from (iii) and (i))

Hence A' and B' are mutually exclusive.

Again,

$\dpi{100} \therefore$ B' $\cap$ C = A $\cap$ C $\dpi{80} \neq$ $\phi$ (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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