If A △ B is defined as (A \ B) ∪ (B \ A), and n(A ∪ B) = 40 and n(A ∩ B) = 13, what is n(A △ B)?
Answer and explanation
Correct answer: 27
The symmetric difference A △ B contains elements that belong to exactly one of A and B. The union contains both exclusive elements and common elements, while the intersection contains only the common elements. Removing the intersection from the union leaves the symmetric difference. Thus n(A △ B) = n(A ∪ B) − n(A ∩ B) = 40 − 13 = 27. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
The symmetric difference A △ B contains elements that belong to exactly one of A and B. The union contains both exclusive elements and common elements, while the intersection contains only the common elements. Removing the intersection from the union leaves the symmetric difference. Thus n(A △ B) = n(A ∪ B) − n(A ∩ B) = 40 − 13 = 27. 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).
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