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

Let A denote the set of the people who like tea & B denote the set of the people who like coffee.

Given :

$n(A \cup B)=70$

$n(A)=52$

$n(B)=37$

To find:

$n(A \cap B)$

We know:

$n(A \cup B)=n(A)+n(B)-n(A \cap B)$

$\Rightarrow 70=52+37-n(A \cap B)$

$\Rightarrow n(A \cap B)=19$

Therefore, 19 people like both tea \& coffee.Given:n(A∪B)=70n(A)=52n(B)=37To find:n(A∩B)We know: n(A∪B)=n(A)+n(B)-n(A∩B)⇒70=52+37-n(A∩B)⇒n(A∩B)=19Therefore, 19 people like both tea & coffee.">iven