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 denote the set of people who like coffee, and T denote the set of people who like tea
`n(CuuT)=70,n(C)=37,n(T)=52`



We know that:

`n(CuuT)=n(C)+n(T)−n(CnnT)`

`∴70=37+52−n(CnnT)`

`⇒70=89−n(C∩T)`

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