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

If Y = {x : x ∈ ℤ, x² < 4}, how many elements does Y have?

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Answer and explanation

Correct answer: 3

For integers, x² < 4 means |x| < 2, or equivalently −2 < x < 2. The integers strictly between −2 and 2 are −1, 0, and 1. Thus Y = {−1, 0, 1}, which contains three elements. The endpoints −2 and 2 are excluded because the inequality is strict, using < rather than ≤.

Tags

setsfinite setintegersinequalityThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

3

Why is this the correct answer?

For integers, x² < 4 means |x| < 2, or equivalently −2 < x < 2. The integers strictly between −2 and 2 are −1, 0, and 1. Thus Y = {−1, 0, 1}, which contains three elements. The endpoints −2 and 2 are excluded because the inequality is strict, using < rather than ≤.

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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