If I₁ = {x : x ∈ ℕ, x ≤ 0}, where ℕ = {1, 2, 3, ...}, which statement about I₁ is correct?
Answer and explanation
Correct answer: I₁ = ∅
The condition requires x to be a natural number and also to satisfy x ≤ 0. Under the definition given in the question, the natural numbers are 1, 2, 3, and so on; none of them is zero or negative. Consequently, no element satisfies both conditions simultaneously. Therefore I₁ contains no elements and is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
I₁ = ∅
Why is this the correct answer?
The condition requires x to be a natural number and also to satisfy x ≤ 0. Under the definition given in the question, the natural numbers are 1, 2, 3, and so on; none of them is zero or negative. Consequently, no element satisfies both conditions simultaneously. Therefore I₁ contains no elements and 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.
