If A = {x ∈ N : x lies between 9 and 10}, what is A?
Answer and explanation
Correct answer: A = ∅
The natural numbers are discrete: consecutive natural numbers do not have another natural number between them. Since 9 and 10 are consecutive, there is no natural number x satisfying 9 < x < 10. The phrase “between 9 and 10” excludes both endpoints, so the set contains no elements and is therefore the empty set ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The natural numbers are discrete: consecutive natural numbers do not have another natural number between them. Since 9 and 10 are consecutive, there is no natural number x satisfying 9 < x < 10. The phrase “between 9 and 10” excludes both endpoints, so the set contains no elements and is therefore 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.
