Question
Download Solution PDFIn a group of 70 persons, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like coffee but NOT tea?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Let A and B denote two sets of elements.
n(A) and n(B) are the numbers of elements present in set A and B respectively.
n(A - B) is the number of elements present in A but NOT in B.
n(B - A) is the number of elements present in B but NOT in A.
n(A ⋃ B) is the total number of elements present in either set A or B.
n(A ⋂ B) is the number of elements present in both the sets A and B.
- n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B)
- n(A - B) = n(A) - n(A ⋂ B)
- n(B - A) = n(B) - n(A ⋂ B)
Calculation:
Let A be the set of people who like coffee and B be the set of people who like tea.
Given that n(A) = 37, n(B) = 52 and n(A ⋃ B) = 70.
Since, every person likes at least one drink (0 elements outside A and B),
we have:
n(A ⋃ B) = n(A) + n(B) - n(A ⋂ B)
⇒ 70 = 37 + 52 - n(A ⋂ B)
⇒ n(A ⋂ B) = 89 - 70 = 19
People who like coffee and NOT tea is given by n(A - B) = n(A) - n(A ⋂ B) = 37 - 19 = 18.
Last updated on Jun 19, 2025
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