If A = {x ∈ ℝ : 0 < x < 0}, what is A?
Answer and explanation
Correct answer: A = ∅
The condition requires one real number x to be greater than 0 and less than 0 at the same time. No real number can satisfy both requirements, because a number cannot lie strictly between two equal endpoints. In interval notation, the condition describes the open interval (0, 0), which contains no points. Hence the solution set A is empty, written as A = ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The condition requires one real number x to be greater than 0 and less than 0 at the same time. No real number can satisfy both requirements, because a number cannot lie strictly between two equal endpoints. In interval notation, the condition describes the open interval (0, 0), which contains no points. Hence the solution set A is empty, written as A = ∅.
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.
