If n(A Δ B) = 54 and n(A ∩ B) = 19, what is n(A ∪ B)?
Answer and explanation
Correct answer: 73
The symmetric difference A Δ B contains the elements belonging to exactly one of the two sets. It is the union of the two exclusive regions, (A − B) ∪ (B − A), and does not include the common region A ∩ B. The union A ∪ B contains those exclusive elements as well as the intersection. Therefore, n(A ∪ B) = n(A Δ B) + n(A ∩ B) = 54 + 19 = 73. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
73
Why is this the correct answer?
The symmetric difference A Δ B contains the elements belonging to exactly one of the two sets. It is the union of the two exclusive regions, (A − B) ∪ (B − A), and does not include the common region A ∩ B. The union A ∪ B contains those exclusive elements as well as the intersection. Therefore, n(A ∪ B) = n(A Δ B) + n(A ∩ B) = 54 + 19 = 73. 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).
