What type of set is A = {x : x ∈ N, 5 < x < 6}?
Answer and explanation
Correct answer: Empty set
The condition requires a natural number strictly greater than 5 and strictly less than 6. Since 5 and 6 are consecutive natural numbers, there is no natural number satisfying both inequalities. Thus A contains no element and is the empty set, written as ∅. It is not a singleton because no value meets the stated condition.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
The condition requires a natural number strictly greater than 5 and strictly less than 6. Since 5 and 6 are consecutive natural numbers, there is no natural number satisfying both inequalities. Thus A contains no element and is the empty set, written as ∅. It is not a singleton because no value meets the stated condition.
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.
