Question

In a survey of 200 students from 7 different schools, 50 people do not play only NFS, 40 people do not play only Dota and 10 people play no online games. Then find the no. of people out of 200 people who do not play both the games.

• A. {3}
• B. {1, 2, 3, 4}
• C. {1, 2, 4, 5}
• D. {1, 2, 3, 4, 5, 6}

Answer 1

The correct option is A

{3}

Let the no. of people who do not play NFS be n(N^I) = 50 (Given)
Similarly no. of people who do not play Dota be n(D^I) = 40 (Given)
And the no. of people who do not play any game n(N^I ∩ D^I) = 10 (Given)
We have to find the no. of people who do not play both the games = n(N∩ D)<sup>I

We know from the Demorgan's law</sup>
(A∩ B)^{I =} A^I ∪ B^I
So, n(N∩ D)^{I =} n(N^I) ∪ n(D^I)

n(N^I) ∪ n(D^I) = n(N^I) + n(D^I) - n(N^I ∩ D^I)

n(N^I) ∪ n(D^I) = 50 + 40 - 10
= 80