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Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 21

If U = ℝ, A = {x : −2 < x ≤ 4} and B = {x : 1 ≤ x < 7}, what is A′ ∪ B′?

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Answer and explanation

Correct answer: (−∞, 1) ∪ (4, ∞)

By De Morgan’s law, A′ ∪ B′ = (A ∩ B)′. The intersection of A = (−2, 4] and B = [1, 7) is [1, 4], because both intervals contain every real number from 1 through 4, including both endpoints. Taking the complement in ℝ excludes [1, 4], giving (−∞, 1) ∪ (4, ∞).

Tags

setscomplementDe Morgans lawintervalsset identitiesMathematicsComplement of a Set and Its PropertiesClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

(−∞, 1) ∪ (4, ∞)

Why is this the correct answer?

By De Morgan’s law, A′ ∪ B′ = (A ∩ B)′. The intersection of A = (−2, 4] and B = [1, 7) is [1, 4], because both intervals contain every real number from 1 through 4, including both endpoints. Taking the complement in ℝ excludes [1, 4], giving (−∞, 1) ∪ (4, ∞).

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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