If A = {x ∈ ℕ : x is greater than 1 and less than 2}, what type of set is A?
Answer and explanation
Correct answer: An empty set
The condition 1 < x < 2 describes numbers strictly between 1 and 2. Although real numbers exist in that interval, no natural number lies strictly between two consecutive natural numbers 1 and 2. Therefore no natural number satisfies the defining condition, so A has no elements and is the empty set, A = ∅.
Frequently asked questions
What is the correct answer to this question?
An empty set
Why is this the correct answer?
The condition 1 < x < 2 describes numbers strictly between 1 and 2. Although real numbers exist in that interval, no natural number lies strictly between two consecutive natural numbers 1 and 2. Therefore no natural number satisfies the defining condition, so A has no elements and is the empty set, A = ∅.
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.
