What is the correct conclusion about A = {x ∈ N : 5 < x < 6}?
Answer and explanation
Correct answer: It is an empty set
The natural numbers are discrete: consecutive natural numbers have no natural number between them. Since 5 and 6 are consecutive, there is no natural number x satisfying the strict inequalities 5 < x < 6. The endpoints are excluded as well. Therefore A has no elements, so it is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
It is an empty set
Why is this the correct answer?
The natural numbers are discrete: consecutive natural numbers have no natural number between them. Since 5 and 6 are consecutive, there is no natural number x satisfying the strict inequalities 5 < x < 6. The endpoints are excluded as well. Therefore A has no elements, so it is the empty set, written as ∅.
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.
