Question

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

Number of students who do not play NFS be n($N^c$) = 50 (Given)
Number of students who do not play Dota be n($D^c$) = 40 (Given)
Number of students who do not play any game n($N^c\cap D^c$) = 10 (Given)
Number of students who do not play both the games = $n(N\cap D{)}^c$

^{We know from the Demorgan's law,}
$(A\cap B{)}^c$ = $A^{c}U{B}^c$
So,

$(N\cap D{)}^c$ = ($N^c$) ∪ ($D^c$)
n($N^c$) ∪ ($D^c$) = n($N^c$) + n($D^c$) - $n(N^c\cap D^c)$
n($N^c$) ∪ ($D^c$) = 50 + 40 - 10
= 80
So, 80 students don't play both the games.