If n(A) = 72, n(B) = 67, and n(A ∪ B) = 101, what is n(A △ B), the number of elements in the symmetric difference of A and B?
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Answer and explanation
Correct answer: 63
First find the intersection using n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus n(A ∩ B) = 72 + 67 − 101 = 38. 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) = 101 − 38 = 63. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
63
Why is this the correct answer?
First find the intersection using n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Thus n(A ∩ B) = 72 + 67 − 101 = 38. 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) = 101 − 38 = 63. 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).
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