In a group of 70 people,37 like coffee,52 lik | vedclass

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Question

(A) Let $A$ be the set of people who like coffee and $B$ be the set of people who like tea.Given that each person likes at least one of the two drinks

Vedclass · Accepted Answer

$19$

Vedclass · Answer

(A) Let $A$ be the set of people who like coffee and $B$ be the set of people who like tea.Given that each person likes at least one of the two drinks,the total number of people is represented by the union of the two sets: $n(A \cup B) = 70$.We are given $n(A) = 37$ and $n(B) = 52$.We use the formula for the union of two sets: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.Substituting the known values into the formula:$70 = 37 + 52 - n(A \cap B)$$70 = 89 - n(A \cap B)$$n(A \cap B) = 89 - 70 = 19$.Therefore,$19$ people like both coffee and tea.

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 people like both coffee and tea?

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