Question

# Out of 200 people, 50 don't play NFS, 40 don't play dota and 10 people play no game. people do not play both NFS and dota.

A
100
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B
80
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C
110
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D
10
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Solution

## The correct option is B 80Let N represent the people who play NFS and D represent the people who play Dota. Given: The no. of people who do not play NFS is n(N') = 50 Similarly, the no. of people who do not play Dota is n(D') = 40 And the no. of people who do not play any game is n(N' ∩ D') = 10 The set of people who play both the games is represented by N∩ D The set of people who do not play both the games is represented by (N∩ D)' Thus, the required number is n(N∩ D)' We know from Demorgan's second law that (A∩ B)' = A' ∪ B' So, n(N∩ D)' = n(N' ∪ D') n(N' ∪ D') = n(N') + n(D') – n(N' ∩ D') n(N' ∪ D') = 50 + 40 – 10 = 80

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