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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 5

If A = {x ∈ ℤ : x² ≤ x}, what is n(A)?

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Answer and explanation

Correct answer: 2

Move all terms to one side: x² − x ≤ 0, which factors as x(x − 1) ≤ 0. The real solution interval is 0 ≤ x ≤ 1. Among integers, the only values in this closed interval are 0 and 1, so A = {0, 1}. Therefore, the number of elements is n(A) = 2. Both endpoints are included because the inequality is non-strict.

Tags

setsfinite setcardinalityintegersThe 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?

2

Why is this the correct answer?

Move all terms to one side: x² − x ≤ 0, which factors as x(x − 1) ≤ 0. The real solution interval is 0 ≤ x ≤ 1. Among integers, the only values in this closed interval are 0 and 1, so A = {0, 1}. Therefore, the number of elements is n(A) = 2. Both endpoints are included because the inequality is non-strict.

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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