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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesHardLevel 21

If U = ℝ and A = (−∞, −5) ∪ [1, 4] ∪ (9, ∞), what is A′?

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Answer and explanation

Correct answer: [−5, 1) ∪ (4, 9]

To find the complement in ℝ, reverse the inclusion of each interval and include the boundary points that were excluded from A. The point −5 is included in the complement, while 1 is excluded because it belongs to A. Similarly, 4 is excluded and 9 is included. Therefore A′ = [−5, 1) ∪ (4, 9].

Tags

setscomplementintervalsreal-numbersComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

[−5, 1) ∪ (4, 9]

Why is this the correct answer?

To find the complement in ℝ, reverse the inclusion of each interval and include the boundary points that were excluded from A. The point −5 is included in the complement, while 1 is excluded because it belongs to A. Similarly, 4 is excluded and 9 is included. Therefore A′ = [−5, 1) ∪ (4, 9].

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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