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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 4

What type of set is Y = {x : x ∈ ℕ and x is divisible by both 2 and 3}?

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Answer and explanation

Correct answer: Infinite set

A natural number divisible by both 2 and 3 is divisible by their least common multiple, 6. The members therefore begin 6, 12, 18, 24, 30, and continue as 6n for every positive natural number n. Since there is no upper bound, infinitely many such numbers exist, so Y is infinite.

Tags

setsinfinite setdivisibilityleast common multipleThe 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?

Infinite set

Why is this the correct answer?

A natural number divisible by both 2 and 3 is divisible by their least common multiple, 6. The members therefore begin 6, 12, 18, 24, 30, and continue as 6n for every positive natural number n. Since there is no upper bound, infinitely many such numbers exist, so Y is infinite.

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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