If n(A) = 88, n(B) = 82, and n(A △ B) = 104, what is n(A ∩ B)?
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Answer and explanation
Correct answer: 33
For finite sets, the symmetric-difference formula is n(A △ B) = n(A) + n(B) − 2n(A ∩ B). Let x = n(A ∩ B). Then 104 = 88 + 82 − 2x = 170 − 2x. Thus 2x = 66 and x = 33. The common elements are subtracted twice because they are included in both n(A) and n(B), so option B is correct.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
For finite sets, the symmetric-difference formula is n(A △ B) = n(A) + n(B) − 2n(A ∩ B). Let x = n(A ∩ B). Then 104 = 88 + 82 − 2x = 170 − 2x. Thus 2x = 66 and x = 33. The common elements are subtracted twice because they are included in both n(A) and n(B), so option B 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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