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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 5

If A = {x ∈ ℕ : x < 1} and B = {x ∈ ℤ : 0 < x < 1}, which statement is correct?

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Answer and explanation

Correct answer: A = B = ∅

Using the usual school convention ℕ = {1, 2, 3, …}, no natural number is less than 1, so A is empty. Also, there is no integer strictly between 0 and 1; consecutive integers have no integer between them. Hence B is empty as well. Therefore, A = B = ∅. The strict inequalities exclude both endpoints.

Tags

setsempty setequal setsnatural numbersThe Empty SetFinite and Infinite Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = B = ∅

Why is this the correct answer?

Using the usual school convention ℕ = {1, 2, 3, …}, no natural number is less than 1, so A is empty. Also, there is no integer strictly between 0 and 1; consecutive integers have no integer between them. Hence B is empty as well. Therefore, A = B = ∅. The strict inequalities exclude both endpoints.

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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