What is correct about F₁ = {x : x ∈ ℕ, x is less than 15 and greater than 15}?
Answer and explanation
Correct answer: It is empty
The condition requires the same natural number x to be less than 15 and greater than 15 simultaneously. No number can satisfy both strict inequalities: a number below 15 cannot also be above 15, and 15 itself is neither less than nor greater than 15. Thus there is no element in F₁, so F₁ = ∅. A set with no elements is called the empty or null set.
Frequently asked questions
What is the correct answer to this question?
It is empty
Why is this the correct answer?
The condition requires the same natural number x to be less than 15 and greater than 15 simultaneously. No number can satisfy both strict inequalities: a number below 15 cannot also be above 15, and 15 itself is neither less than nor greater than 15. Thus there is no element in F₁, so F₁ = ∅. A set with no elements is called the empty or null 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.
