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

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 like both coffee and tea?

Solution:

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.iven

Administrator

Leave a comment

Please enter comment.
Please enter your name.