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Class 10MathematicsSetsComplement of a Set and Its PropertiesHardLevel 21

If U = ℝ, A = (-2, 6], and B = [0, 9), what is A' ∪ B'?

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Answer and explanation

Correct answer: (-∞, 0) ∪ (6, ∞)

Using De Morgan's law, A' ∪ B' = (A ∩ B)'. The intersection of A = (-2, 6] and B = [0, 9) is [0, 6]. Taking its complement in ℝ excludes every number from 0 through 6, including both endpoints. Therefore the result is (-∞, 0) ∪ (6, ∞). The open endpoints are essential.

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setscomplementDe Morgan lawintervalsreal numbersComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

(-∞, 0) ∪ (6, ∞)

Why is this the correct answer?

Using De Morgan's law, A' ∪ B' = (A ∩ B)'. The intersection of A = (-2, 6] and B = [0, 9) is [0, 6]. Taking its complement in ℝ excludes every number from 0 through 6, including both endpoints. Therefore the result is (-∞, 0) ∪ (6, ∞). The open endpoints are essential.

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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