Which statement is correct for the set {x ∈ ℤ : x² = −4}?
Answer and explanation
Correct answer: It is an empty set
For every integer x, the square x² is non-negative: it is either zero or positive. Therefore, no integer can have a square equal to −4. Although complex numbers can solve the equation, the condition specifically restricts x to ℤ, the integers. Hence the defining condition has no allowed solution, so the set is empty and is written as ∅.
Frequently asked questions
What is the correct answer to this question?
It is an empty set
Why is this the correct answer?
For every integer x, the square x² is non-negative: it is either zero or positive. Therefore, no integer can have a square equal to −4. Although complex numbers can solve the equation, the condition specifically restricts x to ℤ, the integers. Hence the defining condition has no allowed solution, so the set is empty and is written as ∅.
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.
