Question

Forty-three persons went to a canteen, which sells soup and tea. If $18$ persons took soup only $8$ took tea only and $5$ took nothing. Use a Venn-diagram to find how many took tea.

Answer 1

Let $U$ be the set of all 43 persons
$S$ be the set of all person who drink soup
$T$ be the set of all person who drink tea
Given,
$n\left(U\right)=43$
$n(S\cap \overline{T})=18$
$n(\overline{S}\cap T)=8$
$n\left(\overline{S\cup T}\right)=5$
Now,
$n(S\cap T)=n\left(U\right)-n(S\cap \overline{T})-n(\overline{S}\cap T)-n\left(\overline{S\cup T}\right)=43-18-8-5=12$
$n\left(T\right)=n(S\cap T)+n(\overline{S}\cap T)=12+8=20$ people took tea.