In a group of 70 people, 37 like coffee, 52 like tea and each person like at least one of the two drinks. The number of persons liking both coffee and tea is 19. State True/false.

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Solution

The correct option is A
16

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

We have, $70 = 37 + 52 - n (A \cap B)$
$n (A \cap B) = 19$ .

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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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In a group of 70 people, 37 like coffee, 52 like tea and each person like at least one of the two drinks. The number of persons liking both coffee and tea is 19. State True/false.

The correct option is A 16 n(A∪B) =n(A)+n(B)−n(A∩B) We have, 70=37+52−n(A∩B) n(A∩B)=19.

The correct option is A
16

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

We have, $70 = 37 + 52 - n (A \cap B)$
$n (A \cap B) = 19$ .