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Class 10MathematicsSetsComplement of a Set and Its PropertiesHardLevel 21

If the universal set is U = R and A = {x ∈ R : |x + 1| ≥ 4}, what is A'?

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Answer and explanation

Correct answer: (-5, 3)

The inequality |x + 1| ≥ 4 means x + 1 ≤ -4 or x + 1 ≥ 4. Therefore A = (-∞, -5] ∪ [3, ∞). Since the universal set is R, its complement consists of the real numbers strictly between -5 and 3: A' = (-5, 3). The endpoints are excluded because they belong to A.

Tags

setsabsolute-valuereal-numberscomplementComplement of a Set and Its PropertiesMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

(-5, 3)

Why is this the correct answer?

The inequality |x + 1| ≥ 4 means x + 1 ≤ -4 or x + 1 ≥ 4. Therefore A = (-∞, -5] ∪ [3, ∞). Since the universal set is R, its complement consists of the real numbers strictly between -5 and 3: A' = (-5, 3). The endpoints are excluded because they belong to A.

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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