Which set is infinite on the real number line?
Answer and explanation
Correct answer: {x ∈ ℝ : 2 < x < 3}
Between any two distinct real numbers, including 2 and 3, there are infinitely many real numbers such as 2.5, 2.25, and 2.125. Therefore {x ∈ ℝ : 2 < x < 3} is an infinite set. Option A contains only 2, option C contains no integer, and option D contains only 2 in ℕ. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
{x ∈ ℝ : 2 < x < 3}
Why is this the correct answer?
Between any two distinct real numbers, including 2 and 3, there are infinitely many real numbers such as 2.5, 2.25, and 2.125. Therefore {x ∈ ℝ : 2 < x < 3} is an infinite set. Option A contains only 2, option C contains no integer, and option D contains only 2 in ℕ. Hence option B is correct.
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.
