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Subjects
Class 10MathematicsSetsComplement of a Set and Its PropertiesMediumLevel 21

If the universal set is U = ℝ and A = {x ∈ ℝ : x < −4 or x ≥ 2}, what is A′?

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Answer and explanation

Correct answer: [−4, 2)

The set A contains all real numbers less than −4 together with all real numbers greater than or equal to 2. Its complement therefore contains the numbers that are not less than −4 and are also less than 2. Thus −4 is included, while 2 is excluded. Consequently, A′ = [−4, 2), so option A is correct.

Tags

setscomplementinterval notationinequalitiesComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

[−4, 2)

Why is this the correct answer?

The set A contains all real numbers less than −4 together with all real numbers greater than or equal to 2. Its complement therefore contains the numbers that are not less than −4 and are also less than 2. Thus −4 is included, while 2 is excluded. Consequently, A′ = [−4, 2), so option A is correct.

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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