Which statement is correct about L = {x : x ∈ R, x² + 1 = 0}?
Answer and explanation
Correct answer: It is an empty set
For every real number x, x² ≥ 0. Consequently, x² + 1 ≥ 1, so the expression can never equal 0. Equivalently, solving the equation gives x² = −1, which has no real solution because the square of a real number cannot be negative. Therefore no real number belongs to L, and L is the empty set. The alternatives involving one, two, or infinitely many elements would require real solutions that do not exist.
Frequently asked questions
What is the correct answer to this question?
It is an empty set
Why is this the correct answer?
For every real number x, x² ≥ 0. Consequently, x² + 1 ≥ 1, so the expression can never equal 0. Equivalently, solving the equation gives x² = −1, which has no real solution because the square of a real number cannot be negative. Therefore no real number belongs to L, and L is the empty set. The alternatives involving one, two, or infinitely many elements would require real solutions that do not exist.
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.
