If n(A △ B) = 64 and n(A − B) = 27, what is n(B − A)?
Answer and explanation
Correct answer: 37
The symmetric difference A △ B consists of the elements that are in A but not in B together with the elements that are in B but not in A. These two parts are disjoint, so n(A △ B) = n(A − B) + n(B − A). Substituting the given values gives 64 = 27 + n(B − A). Hence n(B − A) = 64 − 27 = 37, so option A is correct. The common elements of A and B are excluded from the symmetric difference.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
The symmetric difference A △ B consists of the elements that are in A but not in B together with the elements that are in B but not in A. These two parts are disjoint, so n(A △ B) = n(A − B) + n(B − A). Substituting the given values gives 64 = 27 + n(B − A). Hence n(B − A) = 64 − 27 = 37, so option A is correct. The common elements of A and B are excluded from the symmetric difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
