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Class 10MathematicsSetsVenn DiagramsMediumLevel 10

If n(A ∪ B) = 115, n(A) = 73, n(B) = 67, and n(U) = 150, what is n(Aᶜ ∪ Bᶜ)?

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Answer and explanation

Correct answer: 125

First use the inclusion–exclusion formula: n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 73 + 67 − 115 = 25. By De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. Therefore, n(Aᶜ ∪ Bᶜ) = n(U) − n(A ∩ B) = 150 − 25 = 125. Thus, option D is correct; the original options did not include the mathematically correct value.

Tags

setsvenn diagramsde morgans lawinclusion exclusionMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

125

Why is this the correct answer?

First use the inclusion–exclusion formula: n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 73 + 67 − 115 = 25. By De Morgan’s law, Aᶜ ∪ Bᶜ = (A ∩ B)ᶜ. Therefore, n(Aᶜ ∪ Bᶜ) = n(U) − n(A ∩ B) = 150 − 25 = 125. Thus, option D is correct; the original options did not include the mathematically correct value.

Which subject and chapter does this question cover?

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

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