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 P = set of people who like coffee and Q = set of people like tea.
Then, P ∪ Q = set of people who like at least one of the two drinks.
And P ∩ Q = set of people who like both the drinks.
Given in the question,
n(P) = 37, n(Q) = 52, n(P ∪ Q) = 70.
Use the below formula,
n(P ∪ Q) = n(P) + n(Q) – n(P ∩ Q)
Put the value from the given question,
70 = 37 + 52 – n(P ∩ Q)
⇒ n(P ∩ Q) = 89 – 70 = 19.
∴ 19 people like both coffee and tea.