Let A = {x : x ∈ N, x is a real number greater than 2 and less than 3}. What is the correct conclusion about A?
Answer and explanation
Correct answer: A is the empty set because no natural number lies strictly between 2 and 3
The notation x ∈ N restricts x to natural numbers. Although infinitely many real numbers lie strictly between 2 and 3, there is no natural number in that interval. The endpoints 2 and 3 are also excluded because the inequalities are strict. Therefore no element satisfies every condition, so A = ∅, the empty set.
Frequently asked questions
What is the correct answer to this question?
A is the empty set because no natural number lies strictly between 2 and 3
Why is this the correct answer?
The notation x ∈ N restricts x to natural numbers. Although infinitely many real numbers lie strictly between 2 and 3, there is no natural number in that interval. The endpoints 2 and 3 are also excluded because the inequalities are strict. Therefore no element satisfies every condition, so A = ∅, the empty set.
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.
