If n(A) = 68, n(B) = 53, and n(A ∪ B) = 91, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 30
Apply n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substitution yields n(A ∩ B) = 68 + 53 − 91 = 121 − 91 = 30. The intersection is the part counted in both sets, so it is obtained by removing the union count from the sum of the two individual counts.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
Apply n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Rearranging gives n(A ∩ B) = n(A) + n(B) − n(A ∪ B). Substitution yields n(A ∩ B) = 68 + 53 − 91 = 121 − 91 = 30. The intersection is the part counted in both sets, so it is obtained by removing the union count from the sum of the two individual counts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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