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  4. In a group of 70 people, 37 like coffee, 52 like tea and each person likes atleast one of the two drinks. The number of people who like both coffee and tea, is ...X... . Here, X refers to

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Q. In a group of 70 people, 37 like coffee, 52 like tea and each person likes atleast one of the two drinks. The number of people who like both coffee and tea, is ...X... . Here, $X$ refers to

Sets

Solution:

Let $A$ be the set who like coffee and $B$ be the set who like tea.
Then, $ n(A \cup B)=70, n(A)=37$ and $n(B)=52$
$n(A \cup B) =n(A)+n(B)-n(A \cap B) $
$70 =37+52-n(A \cap B) $
$n(A \cap B) =19$
Thus, 19 people like both coffee and tea.