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

Which option is correct for A = {x ∈ ℝ : x² = 0 and x > 0}?

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Answer and explanation

Correct answer: A = ∅

The equation x² = 0 has exactly one real solution, x = 0. However, the second condition requires x to be strictly greater than 0, and 0 is not greater than 0. Since both conditions must hold simultaneously, no real number satisfies them. Therefore A contains no elements and A = ∅, the empty set.

Tags

setsempty-setreal-numberssimultaneous-conditionsThe 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 = ∅

Why is this the correct answer?

The equation x² = 0 has exactly one real solution, x = 0. However, the second condition requires x to be strictly greater than 0, and 0 is not greater than 0. Since both conditions must hold simultaneously, no real number satisfies them. Therefore A contains no elements and A = ∅, the empty set.

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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