If A = {x : x is an integer greater than 2 and less than 3}, then what is A?
Answer and explanation
Correct answer: A = ∅
The condition requires an integer x to satisfy 2 < x < 3. However, consecutive integers 2 and 3 have no integer strictly between them. The endpoints are excluded because the inequalities are strict. Therefore, no value of x satisfies the condition, so the set contains no elements and is the empty set: A = ∅. Hence, option D is correct.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The condition requires an integer x to satisfy 2 < x < 3. However, consecutive integers 2 and 3 have no integer strictly between them. The endpoints are excluded because the inequalities are strict. Therefore, no value of x satisfies the condition, so the set contains no elements and is the empty set: A = ∅. Hence, option D 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.
