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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 4

For A = {x ∈ ℤ : x² ≤ 1} and B = {−1, 0, 1}, which statement is correct?

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Answer and explanation

Correct answer: A = B

For an integer x, the inequality x² ≤ 1 means −1 ≤ x ≤ 1. The integers in this interval are exactly −1, 0, and 1. Therefore A = {−1, 0, 1}, which is precisely the set B. Hence A and B have the same elements and are equal; omitting 0 or treating the inequality as strict would produce an incorrect result.

Tags

setsequal setsintegersquadratic inequalityThe Empty SetFinite and Infinite Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

For an integer x, the inequality x² ≤ 1 means −1 ≤ x ≤ 1. The integers in this interval are exactly −1, 0, and 1. Therefore A = {−1, 0, 1}, which is precisely the set B. Hence A and B have the same elements and are equal; omitting 0 or treating the inequality as strict would produce an incorrect result.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.

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