What type of set is A = {x ∈ ℝ : x² + 1 ≤ 0}?
Answer and explanation
Correct answer: Empty set
For every real number x, x² is at least 0. Consequently, x² + 1 is at least 1, so it can never be less than or equal to 0. Therefore, no real number satisfies the defining inequality. The set has no elements and is written as A = ∅, so it is the empty set, not a singleton, an infinite set, or the set of all real numbers.
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 + 1 is at least 1, so it can never be less than or equal to 0. Therefore, no real number satisfies the defining inequality. The set has no elements and is written as A = ∅, so it is the empty set, not a singleton, an infinite set, or the set of all real numbers.
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.
