The set {x ∈ ℝ : x² ≤ 0} is equal to which set?
Answer and explanation
Correct answer: {0}
The governing concept is identifying the elements satisfying a condition over the real numbers. For every real x, x² is non-negative, so x² ≤ 0 can occur only when x² = 0. Solving x² = 0 gives the single solution x = 0. Therefore the set is the singleton {0}, and option B is correct. It is not empty because 0 satisfies the condition, and it is not all of ℝ because nonzero real numbers have positive squares.
Frequently asked questions
What is the correct answer to this question?
{0}
Why is this the correct answer?
The governing concept is identifying the elements satisfying a condition over the real numbers. For every real x, x² is non-negative, so x² ≤ 0 can occur only when x² = 0. Solving x² = 0 gives the single solution x = 0. Therefore the set is the singleton {0}, and option B is correct. It is not empty because 0 satisfies the condition, and it is not all of ℝ because nonzero real numbers have positive squares.
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.
