In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks… · ABC26GN0872

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 $=19$.