In a Venn diagram, n(A Δ B) = 96 and n(A ∪ B) = 137. What is n(A ∩ B)?
Advertisement
Answer and explanation
Correct answer: 41
The symmetric difference A Δ B consists of elements that are in A or B but not in both. Thus, A ∪ B is partitioned into two disjoint parts: A Δ B and A ∩ B. Therefore, n(A ∪ B) = n(A Δ B) + n(A ∩ B). Substituting the values gives 137 = 96 + n(A ∩ B), so n(A ∩ B) = 137 − 96 = 41. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
41
Why is this the correct answer?
The symmetric difference A Δ B consists of elements that are in A or B but not in both. Thus, A ∪ B is partitioned into two disjoint parts: A Δ B and A ∩ B. Therefore, n(A ∪ B) = n(A Δ B) + n(A ∩ B). Substituting the values gives 137 = 96 + n(A ∩ B), so n(A ∩ B) = 137 − 96 = 41. Hence, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement