Under the usual school convention ℕ = {1, 2, 3, ...}, which statement is correct for A = {x ∈ ℕ : x < 1}?
Answer and explanation
Correct answer: A = ∅, an empty and finite set
Under the convention stated in the question, the natural numbers begin with 1. Every natural number is therefore at least 1, so no natural number satisfies x < 1. Consequently A contains no elements and is the empty set, ∅. The empty set has cardinality 0, and it is classified as finite because its number of elements is bounded.
Frequently asked questions
What is the correct answer to this question?
A = ∅, an empty and finite set
Why is this the correct answer?
Under the convention stated in the question, the natural numbers begin with 1. Every natural number is therefore at least 1, so no natural number satisfies x < 1. Consequently A contains no elements and is the empty set, ∅. The empty set has cardinality 0, and it is classified as finite because its number of elements is bounded.
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.
