Answer: Option A
:
A
Let the numberof 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, thenumberof 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 numberof 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, $n\left(\right(N\cap D{)}^{\prime })=n(N^{\prime }\cup D^{\prime })=n(N^{\prime })+n(D^{\prime })-n(N^{\prime }\cap D^{\prime })$
$=50+40-10$
$=80$