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Subjects
Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 3

If A = {x : x ∈ Z and x² ≤ 9}, how many elements does A have?

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Answer and explanation

Correct answer: 7

Since x² ≤ 9, taking square roots gives -3 ≤ x ≤ 3. The set is restricted to integers, so its elements are {-3, -2, -1, 0, 1, 2, 3}. There are seven elements in total. The endpoints -3 and 3 must be included because the inequality is less than or equal to, not strictly less than.

Tags

setsfinite-setintegersquadratic-inequalityThe 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?

7

Why is this the correct answer?

Since x² ≤ 9, taking square roots gives -3 ≤ x ≤ 3. The set is restricted to integers, so its elements are {-3, -2, -1, 0, 1, 2, 3}. There are seven elements in total. The endpoints -3 and 3 must be included because the inequality is less than or equal to, not strictly less 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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