If n(A ∪ B) = 60, n(A − B) = 18, and n(B − A) = 22, what is n(A ∩ B)?
Answer and explanation
Correct answer: 20
The union A ∪ B can be partitioned into three mutually disjoint parts: the elements only in A, represented by A − B; the elements only in B, represented by B − A; and the elements common to both, represented by A ∩ B. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 60 = 18 + 22 + n(A ∩ B), so n(A ∩ B) = 20. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The union A ∪ B can be partitioned into three mutually disjoint parts: the elements only in A, represented by A − B; the elements only in B, represented by B − A; and the elements common to both, represented by A ∩ B. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 60 = 18 + 22 + n(A ∩ B), so n(A ∩ B) = 20. Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
