If n(A) = 56, n(B) = 61, n(A − B) = 19, and n(B − A) = 24, what is n(A ∩ B)?
Answer and explanation
Correct answer: 37
The set A consists of the elements only in A, represented by A − B, together with the elements common to both sets, represented by A ∩ B. Therefore, n(A) = n(A − B) + n(A ∩ B), so n(A ∩ B) = 56 − 19 = 37. We can verify the result using set B: n(B) = n(B − A) + n(A ∩ B), giving 61 − 24 = 37. Since both calculations agree, the correct answer is option B, 37.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
The set A consists of the elements only in A, represented by A − B, together with the elements common to both sets, represented by A ∩ B. Therefore, n(A) = n(A − B) + n(A ∩ B), so n(A ∩ B) = 56 − 19 = 37. We can verify the result using set B: n(B) = n(B − A) + n(A ∩ B), giving 61 − 24 = 37. Since both calculations agree, the correct answer is option B, 37.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
