If n(A) = 39, n(B) = 44, and 51 elements lie in exactly one of the two sets, what is n(A ∩ B)?
Answer and explanation
Correct answer: 16
Let x = n(A ∩ B). The elements that lie in exactly one of the two sets are the elements in A but not B plus the elements in B but not A. Their number is (39 − x) + (44 − x) = 83 − 2x. Since this number is 51, we obtain 83 − 2x = 51, so 2x = 32 and x = 16. Therefore, n(A ∩ B) = 16 and option B is correct. This is also consistent with the formula for symmetric difference.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Let x = n(A ∩ B). The elements that lie in exactly one of the two sets are the elements in A but not B plus the elements in B but not A. Their number is (39 − x) + (44 − x) = 83 − 2x. Since this number is 51, we obtain 83 − 2x = 51, so 2x = 32 and x = 16. Therefore, n(A ∩ B) = 16 and option B is correct. This is also consistent with the formula for symmetric difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
