If A = {x ∈ N : x is less than every natural number}, what is A?
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Answer and explanation
Correct answer: A = ∅
An element of A would have to be less than every natural number, including itself. However, no number is less than itself because the relation x < x is always false. Therefore, regardless of whether a textbook begins N with 0 or 1, no natural number satisfies the condition, so A is the empty set.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
An element of A would have to be less than every natural number, including itself. However, no number is less than itself because the relation x < x is always false. Therefore, regardless of whether a textbook begins N with 0 or 1, no natural number satisfies the condition, so A is the empty 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.
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