If A = {x : x ∈ Z, x² = −4}, what kind of set is A?
Advertisement
Answer and explanation
Correct answer: Empty set
For every integer x, the square x² is non-negative: it is either zero or positive. It can never equal −4. Although the equation has complex solutions, the set is restricted to integers, so those solutions are not allowed. Hence no integer satisfies the condition and A is the empty set.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
For every integer x, the square x² is non-negative: it is either zero or positive. It can never equal −4. Although the equation has complex solutions, the set is restricted to integers, so those solutions are not allowed. Hence no integer satisfies the condition and A is the empty set.
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.
Advertisement