Question

In a survey of 300 android mobile users, who make video calls, 75 people said they use only viber, 45 use only skype and 90 people use both. The number of persons who use neither viber nor skype is __.

Answer 1

Let U denote the set of surveyed mobile users. V denote set of people using Viber and S denote set of people using Skype. Then, n(U) = 300, n(V ∩ S) = 90
Number of persons using Viber = Number of persons using only Viber + Number of persons using both Viber and Skype
Therefore, n(V)=75+90=165
Number of persons using Skype = Number of persons using only Skype + Number of persons using both Viber and Skype
Therefore, n(S)=45+90=135

Now, no. of persons who use neither viber nor skype is given as,
$n(\overline{V}\cap \overline{S})=n\left(\overline{V\cup S}\right)=n\left(U\right)-n\left(VUS\right)=n\left(U\right)-\left[n\right(V)+n(S)-n(V\cap S\left)\right]=300-(165+135-90)=300-210=90$