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?

Explanation

Let C be the set of people who like coffe and T be the set of people who like tea.
`:. n(C)=37,n(T)=52`
and `n(C cupT)=70`
`:. n(C cupT)=n(C) +n(T)-n(C cap T)`
`rArr 70=37+52-n(C cap T)`
`rArr n(C cap T) = 89-70 = 19`
Therefore, the number of people who like both coffee and tea are 19.