Question
Download Solution PDF22 students play cricket and 11 play football from the class of 25, then how many of them play both cricket and football. Given each student play at least one of the sports.
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 of 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 is the students who play cricket, so n(A) = 22
Set B is the students who play football, so n(B) = 11
Set of all students A ∪ B, so n(A ∪ B) = 25
∵ n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
⇒ 25 = 22 + 11 - n(A ∩ B)
⇒ n(A ∩ B) = 33 - 25 = 8
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