Which option is correct about the open interval (2, 2)?
Answer and explanation
Correct answer: It is the empty set
The open interval (2, 2) consists of real numbers x satisfying 2 < x < 2. No real number can be simultaneously greater than 2 and less than 2. Therefore, the interval contains no elements and is the empty set, written as ∅. The endpoint 2 is excluded by open brackets, and in any case it cannot satisfy both strict inequalities.
Frequently asked questions
What is the correct answer to this question?
It is the empty set
Why is this the correct answer?
The open interval (2, 2) consists of real numbers x satisfying 2 < x < 2. No real number can be simultaneously greater than 2 and less than 2. Therefore, the interval contains no elements and is the empty set, written as ∅. The endpoint 2 is excluded by open brackets, and in any case it cannot satisfy both strict inequalities.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
