If N = {1, 2, 3, …}, what type of set is {x : x ∈ N, x < 1}?
Answer and explanation
Correct answer: Empty set
Under the stated convention, the natural numbers begin with 1. Every natural number is therefore at least 1, so none of them can satisfy x < 1. Since the defining condition has no solution in N, the set contains no elements and is the empty set, written as ∅. It is finite with cardinality zero.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
Under the stated convention, the natural numbers begin with 1. Every natural number is therefore at least 1, so none of them can satisfy x < 1. Since the defining condition has no solution in N, the set contains no elements and is the empty set, written as ∅. It is finite with cardinality zero.
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.
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