In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. Find the number of people who like both coffee and tea.
Answer
Answer (as printed):
Explanation
Let $A$ and $B$ represent the set of people who like coffee and tea respectively. Then, $n(A)=37, n(B)=52, n(A \cup B)=70$. $$\begin{aligned} \therefore \quad n(A \cap B) & =n(A)+n(B)-n(A \cup B) \\ & =37+52-70=89-70=19 . \end{aligned}$$ Hence, number of people who like both coffee and tea $=19$.
Explanation as extracted from the printed page; notation may be imperfect.