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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 4

If F₁ = {x : x ∈ ℝ and x² + 4 = 0}, what is F₁?

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Answer and explanation

Correct answer: Empty set

For every real number x, x² is at least 0. Consequently, x² + 4 is at least 4, so it can never equal 0. Equivalently, the equation would require x² = −4, which has no real solution. Since F₁ contains real numbers satisfying the condition and there are none, F₁ = ∅, the empty set.

Tags

setsempty setreal numbersquadratic equationsThe 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?

Empty set

Why is this the correct answer?

For every real number x, x² is at least 0. Consequently, x² + 4 is at least 4, so it can never equal 0. Equivalently, the equation would require x² = −4, which has no real solution. Since F₁ contains real numbers satisfying the condition and there are none, F₁ = ∅, 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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