NCERT Class XI Mathematics - Sets - Solutions
© examsnet.com
Question : 55
Total: 73
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?
Solution:
Let C be the set of persons who like coffee and T be the set of persons who like tea. ∴ n(C) = 37, n(T) = 52 and n(C ∪ T) = 70
We know that
n(C ∪ T) = n(C) + n(T) – n(C ∩ T)
⇒ 70 = 37 + 52 – n(C ∩ T) ∴ n(C ∩ T) = 89 – 70 = 19.
We know that
n(C ∪ T) = n(C) + n(T) – n(C ∩ T)
⇒ 70 = 37 + 52 – n(C ∩ T) ∴ n(C ∩ T) = 89 – 70 = 19.
© examsnet.com
Go to Question: