Which of the following is not an empty set?
Answer and explanation
Correct answer: {x ∈ ℕ : x + 2 = 5}
A set is empty when no element satisfies its defining condition. In option A, x² = 0 gives x = 0; depending on the convention for natural numbers, this may be considered empty if ℕ starts at 1. Options B and D are clearly empty because no integer lies strictly between 0 and 1 and no natural number is negative. In option C, x + 2 = 5 gives x = 3, and 3 is a natural number. Therefore, option C contains one element and is not empty.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℕ : x + 2 = 5}
Why is this the correct answer?
A set is empty when no element satisfies its defining condition. In option A, x² = 0 gives x = 0; depending on the convention for natural numbers, this may be considered empty if ℕ starts at 1. Options B and D are clearly empty because no integer lies strictly between 0 and 1 and no natural number is negative. In option C, x + 2 = 5 gives x = 3, and 3 is a natural number. Therefore, option C contains one element and is not empty.
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.
