Question

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Answer 1

Let C be the set of persons who like coffee and T be the set of persons who like tea.

$\therefore$ $n\left(C\right)=37,n\left(T\right)=52$

and $n(C\cup T)=70$

We know that

$n(C\cup T)=n\left(C\right)+n\left(T\right)-n(C\cap T)$

$\therefore$ $70=37+52-n(C\cap T)$

$\therefore$ $n(C\cap T)=89-70=19.$