Discussion
In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both cold and hot drinks?
Answer: B
Let C be the set of people who like cold drinks and H be the set of people who like hot drinks.
n(C) = 27, n(H) = 42.
Since each person likes at least one drink, the union is the total number of people: n(C ∪ H) = 60.
Using the formula n(C ∪ H) = n(C) + n(H) - n(C ∩ H):
60 = 27 + 42 - n(C ∩ H)
60 = 69 - n(C ∩ H)
n(C ∩ H) = 69 - 60 = 9.
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