Which of the following sets is empty?
Answer and explanation
Correct answer: C = {x : x ∈ N, x² = -1}
The governing concept is the empty set: it has no element satisfying its defining condition. For every natural number x, x² is non-negative, so x² = -1 has no natural-number solution. Therefore C contains no element and is empty. In contrast, A contains 4, B contains -4 and 4, and D contains 0 and 1. Hence option C is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
C = {x : x ∈ N, x² = -1}
Why is this the correct answer?
The governing concept is the empty set: it has no element satisfying its defining condition. For every natural number x, x² is non-negative, so x² = -1 has no natural-number solution. Therefore C contains no element and is empty. In contrast, A contains 4, B contains -4 and 4, and D contains 0 and 1. Hence option C is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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