Which option represents a non-empty set containing exactly one element?
Advertisement
Answer and explanation
Correct answer: {x ∈ ℤ : x² = 9 and x > 0}
For option B, x² = 9 gives x = 3 or x = −3. The additional condition x > 0 excludes −3 and leaves only x = 3, so the set is {3}. It is non-empty and has exactly one element, making it a singleton set. Option A is empty, option C has two elements, and option D is infinite.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℤ : x² = 9 and x > 0}
Why is this the correct answer?
For option B, x² = 9 gives x = 3 or x = −3. The additional condition x > 0 excludes −3 and leaves only x = 3, so the set is {3}. It is non-empty and has exactly one element, making it a singleton set. Option A is empty, option C has two elements, and option D is infinite.
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