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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)HardLevel 17

If A △ B = (A − B) ∪ (B − A), n(A △ B) = 26, and n(A ∩ B) = 9, what is n(A ∪ B)?

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Answer and explanation

Correct answer: 35

The symmetric difference A △ B contains the elements that belong to exactly one of A or B, while A ∩ B contains the elements common to both. These two parts are disjoint and together make up A ∪ B. Therefore, n(A ∪ B) = n(A △ B) + n(A ∩ B) = 26 + 9 = 35. Hence option A is correct.

Tags

setssymmetric-differencecardinalityunionintersectionoperations-on-setsOperations on Sets (UnionDifference)operations on sets union intersection difference

Frequently asked questions

What is the correct answer to this question?

35

Why is this the correct answer?

The symmetric difference A △ B contains the elements that belong to exactly one of A or B, while A ∩ B contains the elements common to both. These two parts are disjoint and together make up A ∪ B. Therefore, n(A ∪ B) = n(A △ B) + n(A ∩ B) = 26 + 9 = 35. 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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