In a class, n(A) = 86, n(B) = 78, and the number of students in exactly one set is 98. What is n(A ∩ B)?
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Answer and explanation
Correct answer: 33
Let n(A ∩ B) = x. Students in exactly one set are counted in A only and B only, so their number is n(A) + n(B) − 2n(A ∩ B). Thus, 98 = 86 + 78 − 2x = 164 − 2x. Hence, 2x = 66 and x = 33. Equivalently, the common students are counted twice in n(A) + n(B), so twice the intersection must be removed. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
Let n(A ∩ B) = x. Students in exactly one set are counted in A only and B only, so their number is n(A) + n(B) − 2n(A ∩ B). Thus, 98 = 86 + 78 − 2x = 164 − 2x. Hence, 2x = 66 and x = 33. Equivalently, the common students are counted twice in n(A) + n(B), so twice the intersection must be removed. Option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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