If n(A ∪ B) = 48, n(A − B) = 20, and n(B − A) = 13, what is n(A ∩ B)?
Advertisement
Answer and explanation
Correct answer: 15
For two sets, the union consists of three mutually exclusive regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 48 = 20 + 13 + n(A ∩ B), so n(A ∩ B) = 48 − 33 = 15. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
For two sets, the union consists of three mutually exclusive regions: the elements only in A, the elements only in B, and the elements common to both sets. Therefore, n(A ∪ B) = n(A − B) + n(B − A) + n(A ∩ B). Substituting the given values gives 48 = 20 + 13 + n(A ∩ B), so n(A ∩ B) = 48 − 33 = 15. Hence, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement