Which statement is correct about A = {x : x ∈ ℕ and x² + 1 = 0}?
Answer and explanation
Correct answer: It is an empty set
Solving x² + 1 = 0 gives x² = −1. For every natural number x, x² is non-negative, so it can never equal −1. Hence no natural number satisfies the defining equation. A set whose defining condition has no solution is the empty set. Therefore A = ∅, and the correct statement is that A is an empty set, represented by option A.
Frequently asked questions
What is the correct answer to this question?
It is an empty set
Why is this the correct answer?
Solving x² + 1 = 0 gives x² = −1. For every natural number x, x² is non-negative, so it can never equal −1. Hence no natural number satisfies the defining equation. A set whose defining condition has no solution is the empty set. Therefore A = ∅, and the correct statement is that A is an empty set, represented by option A.
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.
