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Class 10MathematicsSetsVenn DiagramsEasyLevel 14

If n(A ∪ B) = 96, n(A) = 58, and n(B) = 49, find n(A ∩ B).

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Answer and explanation

Correct answer: 11

For two finite sets, the inclusion-exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 96 = 58 + 49 − n(A ∩ B). Therefore, n(A ∩ B) = 107 − 96 = 11. The subtraction removes the double counting of common elements, so option A is correct.

Tags

setsVenn diagramsintersectioninclusion-exclusionMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

11

Why is this the correct answer?

For two finite sets, the inclusion-exclusion formula is n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Substituting the given values gives 96 = 58 + 49 − n(A ∩ B). Therefore, n(A ∩ B) = 107 − 96 = 11. The subtraction removes the double counting of common elements, so option A is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.

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