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

Which set is A = {x ∈ ℕ : x² < 2x} equal to?

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Answer and explanation

Correct answer: A = {1}

Rewrite the inequality as x² − 2x < 0, or x(x − 2) < 0. Over the real numbers, this holds when 0 < x < 2. The natural numbers in this open interval depend on the usual school convention ℕ = {1, 2, 3, …}; only x = 1 belongs to it. Therefore, A = {1}. Neither 0 nor 2 satisfies the strict inequality.

Tags

setsfinite setsingleton setinequalityThe 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?

A = {1}

Why is this the correct answer?

Rewrite the inequality as x² − 2x < 0, or x(x − 2) < 0. Over the real numbers, this holds when 0 < x < 2. The natural numbers in this open interval depend on the usual school convention ℕ = {1, 2, 3, …}; only x = 1 belongs to it. Therefore, A = {1}. Neither 0 nor 2 satisfies the strict inequality.

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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