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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 6

If J₁ = {x : x ∈ ℤ, |x| < 3}, how many elements does J₁ have?

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Answer and explanation

Correct answer: 5

For an integer x, the inequality |x| < 3 is equivalent to -3 < x < 3. The integers strictly between -3 and 3 are -2, -1, 0, 1, and 2. Thus J₁ = {-2, -1, 0, 1, 2}, which contains five distinct elements. The endpoints -3 and 3 are excluded because the inequality is strict, so the correct answer is 5.

Tags

setsfinite setabsolute valueintegersThe 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?

5

Why is this the correct answer?

For an integer x, the inequality |x| < 3 is equivalent to -3 < x < 3. The integers strictly between -3 and 3 are -2, -1, 0, 1, and 2. Thus J₁ = {-2, -1, 0, 1, 2}, which contains five distinct elements. The endpoints -3 and 3 are excluded because the inequality is strict, so the correct answer is 5.

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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