Question

Of a total of 300 users who make video calls, 75 people use Viber, 45 use Skype and 30 use both. The no. of people who use neither Viber nor Skype is

• A. $210$
• B. $150$
• C. $270$

Answer 1

The correct option is A $210$

Let $U$ denote the set of surveyed mobile users (the universal set), $V$ the set of people using viber and $S$, the set of people using skype. Then, by question, we have $n\left(U\right)=300$, $n\left(V\right)=75$, $n\left(S\right)=45$ and $n(V\cap S)=30$
Now, the number of people who use neither viber nor skype is given by $n(V^{\prime }\cap S^{\prime })$
But by de-Morgan's law, we have $V^{\prime }\cap S^{\prime }=(V\cup S{)}^{\prime }$
$⟹n(V^{\prime }\cap S^{\prime })=n\left(\right(V\cup S{)}^{\prime })$
But $n\left(\right(V\cup S{)}^{\prime })=n(U)-n(V\cup S)$
$=n\left(U\right)-\left[n\right(V)+n(S)-n(V\cap S\left)\right]$
$=300-(75+45-30)=300-90=210$