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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)EasyLevel 18

If A ∩ B = ∅, n(A) = 9, and n(B) = 11, what is n(A ∪ B)?

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Answer and explanation

Correct answer: 20

For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since A ∩ B = ∅, its cardinality is zero. Thus n(A ∪ B) = 9 + 11 − 0 = 20. Equivalently, because the sets are disjoint, no element is counted twice, so their cardinalities can be added directly. Therefore, option B is correct.

Tags

setsunioncardinalityinclusion-exclusionOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

20

Why is this the correct answer?

For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Since A ∩ B = ∅, its cardinality is zero. Thus n(A ∪ B) = 9 + 11 − 0 = 20. Equivalently, because the sets are disjoint, no element is counted twice, so their cardinalities can be added directly. Therefore, option B 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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