Question
Download Solution PDFIn a class of 50, 20 students like mathematics, 15 like science and 5 like both mathematics and science. Find the number of students who do not like any of the 2 subjects.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Set theory:
- A ∪ B means set of all the values in the set A and B.
- A ∩ B is the set of common elements in A and B.
- Subset (⊂) is the set such that all the elements of the subset are in the set from which the subset is taken from.
- Number of elements in set A = n(A)
- n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
- A' = U - A, where U is a universal set given and A is any set
- A - B = set values of set A not in set B
Calculation:
Set A of students who like mathematics, so n(A) = 20
Set B of students who like science, so n(B) = 15
Given n(A ∩ B) = 5
Set of students who like at least one of the 2 given subjects is A∪B
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A ∪ B) = 20 + 15 - 5 = 30
Students who do not like either of the subjects = Total students - n(A ∪ B)
N = 50 - 30 = 20
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