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

If A ∩ B = ∅, n(A) = p, and n(B) = q, what is n(A ∪ B)?

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Answer and explanation

Correct answer: p + q

For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Here A ∩ B is the empty set, so it has zero elements: n(A ∩ B) = 0. Substituting the given values gives n(A ∪ B) = p + q − 0 = p + q. Because the sets are disjoint, no common element is counted twice.

Tags

setsdisjoint-setscardinalityunioncountingOperations on Sets (UnionIntersectionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

p + q

Why is this the correct answer?

For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Here A ∩ B is the empty set, so it has zero elements: n(A ∩ B) = 0. Substituting the given values gives n(A ∪ B) = p + q − 0 = p + q. Because the sets are disjoint, no common element is counted twice.

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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