Which of the following is an empty set? Assume N = {1, 2, 3, ...}.
Answer and explanation
Correct answer: {x ∈ N : x < 1}
Under the stated convention, N = {1, 2, 3, ...}, so no natural number is less than 1. Therefore the set in option A has no elements and is empty. Option B contains 0, option C contains 1, and option D also contains the integer 0. Specifying the convention for N removes any ambiguity about whether zero is included.
Frequently asked questions
What is the correct answer to this question?
{x ∈ N : x < 1}
Why is this the correct answer?
Under the stated convention, N = {1, 2, 3, ...}, so no natural number is less than 1. Therefore the set in option A has no elements and is empty. Option B contains 0, option C contains 1, and option D also contains the integer 0. Specifying the convention for N removes any ambiguity about whether zero is included.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
