Over the real numbers, what is the type of the set {x ∈ R : x² + 1 = 0}?
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Answer and explanation
Correct answer: The empty set
For every real number x, x² is non-negative, so x² + 1 is at least 1. It can therefore never equal zero. Equivalently, the equation x² + 1 = 0 would require x² = -1, which has no real solution. Since no real number satisfies the condition, the set contains no elements and is empty.
Frequently asked questions
What is the correct answer to this question?
The empty set
Why is this the correct answer?
For every real number x, x² is non-negative, so x² + 1 is at least 1. It can therefore never equal zero. Equivalently, the equation x² + 1 = 0 would require x² = -1, which has no real solution. Since no real number satisfies the condition, the set contains no elements and is empty.
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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