Which set is not equal to ℤ but is still infinite?
Answer and explanation
Correct answer: {x ∈ ℤ : x ≥ 0}
The set in option A is {0, 1, 2, 3, ...}, which continues without end and is therefore infinite. It is not equal to ℤ because ℤ also contains negative integers such as −1 and −2, while option A does not. Option B is finite, option C equals {−1, 1}, and option D is empty because no integer lies strictly between 0 and 1.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℤ : x ≥ 0}
Why is this the correct answer?
The set in option A is {0, 1, 2, 3, ...}, which continues without end and is therefore infinite. It is not equal to ℤ because ℤ also contains negative integers such as −1 and −2, while option A does not. Option B is finite, option C equals {−1, 1}, and option D is empty because no integer lies strictly between 0 and 1.
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.
