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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 19

If U = {1, 2, ..., 12}, A = {1, 3, 5, 7, 9, 11}, and B = {2, 3, 5, 7, 11}, what is (A′ ∪ B′)′?

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Answer and explanation

Correct answer: {3, 5, 7, 11}

All complements are taken with respect to the universal set U. By De Morgan’s law, (A′ ∪ B′)′ = A ∩ B. The intersection contains exactly those elements common to both A and B. Comparing the two sets, the common elements are 3, 5, 7, and 11. Therefore, the correct answer is option A: {3, 5, 7, 11}.

Tags

setsDe Morgan's lawscomplement of a setintersectionMathematics Class 10Complement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{3, 5, 7, 11}

Why is this the correct answer?

All complements are taken with respect to the universal set U. By De Morgan’s law, (A′ ∪ B′)′ = A ∩ B. The intersection contains exactly those elements common to both A and B. Comparing the two sets, the common elements are 3, 5, 7, and 11. Therefore, the correct answer is option A: {3, 5, 7, 11}.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.

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