If S = {x : x ∈ N and x < 1}, where N = {1, 2, 3, ...}, what type of set is S?
Answer and explanation
Correct answer: Empty set
The smallest natural number under the stated convention is 1. The condition x < 1 therefore has no natural-number solution, because every natural number is at least 1. Hence S contains no element and is the empty set, written as ∅. It is not a singleton, since a singleton must contain exactly one element.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
The smallest natural number under the stated convention is 1. The condition x < 1 therefore has no natural-number solution, because every natural number is at least 1. Hence S contains no element and is the empty set, written as ∅. It is not a singleton, since a singleton must contain exactly one element.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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