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?

Let C denote the set of people who like coffee, and T denote the set of people who like tea.
n(C ∪ T) = 70, n(C) = 37, n(T) = 52
We know that:
n(C ∪ T) = n(C) + n(T) - n(C ∩ T)
∴ 70 = 37 + 52 - n(C ∩ T)
⇒ 70 = 89 - n(C ∩ T)
⇒ n(C ∩ T) = 89 - 70 = 19
Thus, 19 people like both coffee and tea