Question

In a survey of 200 students from 7 different schools, 50 people do not play NFS, 40 people do not play Dota and 10 people do not play any online game. Find the number of people who do not play both the games.

• A. 80
• B. 70
• C. 60
• D. 50

Answer 1

The correct option is A

80

Let the number of people who do not play NFS be n(N') = 50. (Given)
Similarly, the number of people who do not play Dota be n(D') = 40. (Given)
And, the number of people who do not play any game be n((N ∪ D)')=n(N' ∩ D') = 10. (Given) (de-Morgan's law)
We have to find the number of people who do not play both the games = n(N∩ D)'.

We know from de-Morgan's law that for sets A and B,
$(A\cap B{)}^{\prime }=A^{\prime }\cup B^{\prime }.$
So, $n\left(\right(N\cap D{)}^{\prime })=n(N^{\prime }\cup D^{\prime })=n(N^{\prime })+n(D^{\prime })-n(N^{\prime }\cap D^{\prime })$
$=50+40-10$
$=80$