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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 10

What kind of set is A = {x : x ∈ ℕ, x ≤ 0}, assuming ℕ = {1, 2, 3, ...}?

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Answer and explanation

Correct answer: Empty set

Under the stated convention, the natural numbers are 1, 2, 3, and so on; zero and negative numbers are not included. Every natural number is therefore greater than 0 and fails the condition x ≤ 0. No element satisfies the rule, so A = ∅, the empty set. Hence option A is correct.

Tags

setsempty-setnatural-numbersset-builder-notationThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

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 are 1, 2, 3, and so on; zero and negative numbers are not included. Every natural number is therefore greater than 0 and fails the condition x ≤ 0. No element satisfies the rule, so A = ∅, the empty set. Hence option A is correct.

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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