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Class 10MathematicsSetsVenn DiagramsMediumLevel 14

If n(U) = 240, n(A ∪ B) = 157, and n(Aᶜ ∩ Bᶜ) = 83, which relation is true?

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Answer and explanation

Correct answer: n(A ∪ B) + n(Aᶜ ∩ Bᶜ) = n(U)

By De Morgan’s law, Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ. Therefore, the sets A ∪ B and Aᶜ ∩ Bᶜ are complementary regions of the universal set U. Their cardinalities add to n(U): 157 + 83 = 240. Hence option A is the only true relation; the other options confuse intersection, union, or equality of unrelated regions.

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setsvenn diagramscomplementDe Morgan lawMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

n(A ∪ B) + n(Aᶜ ∩ Bᶜ) = n(U)

Why is this the correct answer?

By De Morgan’s law, Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ. Therefore, the sets A ∪ B and Aᶜ ∩ Bᶜ are complementary regions of the universal set U. Their cardinalities add to n(U): 157 + 83 = 240. Hence option A is the only true relation; the other options confuse intersection, union, or equality of unrelated regions.

Which subject and chapter does this question cover?

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

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