If n(A) = 64, n(B) = 59, and n(A ∪ B) = 91, what is n(A △ B)?
Advertisement
Answer and explanation
Correct answer: 59
Use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, n(A ∩ B) = 64 + 59 − 91 = 32. The symmetric difference A △ B contains elements belonging to exactly one of the two sets, so n(A △ B) = n(A ∪ B) − n(A ∩ B) = 91 − 32 = 59. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
59
Why is this the correct answer?
Use the inclusion–exclusion formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Therefore, n(A ∩ B) = 64 + 59 − 91 = 32. The symmetric difference A △ B contains elements belonging to exactly one of the two sets, so n(A △ B) = n(A ∪ B) − n(A ∩ B) = 91 − 32 = 59. Hence, 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).
Advertisement