Discussion
Out of 120 customers at a restaurant, 93 have a coffee and 47 have a tea. Assuming every customer has at least one beverage, find the number of customers who have a coffee but not tea.
Answer: D
Let C be for coffee and T be for tea.
n(C) = 93, n(T) = 47, n(C ∪ T) = 120.
First, find the number of customers who have both: n(C ∩ T).
n(C ∪ T) = n(C) + n(T) - n(C ∩ T)
120 = 93 + 47 - n(C ∩ T)
120 = 140 - n(C ∩ T)
n(C ∩ T) = 140 - 120 = 20.
Number of customers who have only coffee = n(C) - n(C ∩ T) = 93 - 20 = 73.
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