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Class 10MathematicsSetsSets and their representationsEasyLevel 1

If C₂ = {x ∈ ℕ : x is divisible by both 2 and 3 and x ≤ 18}, then what is C₂?

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Answer and explanation

Correct answer: {6, 12, 18}

A natural number divisible by both 2 and 3 must be divisible by their least common multiple, lcm(2, 3) = 6. The positive multiples of 6 not exceeding 18 are 6, 12, and 18. Therefore C₂ = {6, 12, 18}. Numbers divisible by only one of 2 or 3 do not satisfy the word both.

Tags

setsdivisibilitymultiplesleast-common-multipleSets and their representationsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

{6, 12, 18}

Why is this the correct answer?

A natural number divisible by both 2 and 3 must be divisible by their least common multiple, lcm(2, 3) = 6. The positive multiples of 6 not exceeding 18 are 6, 12, and 18. Therefore C₂ = {6, 12, 18}. Numbers divisible by only one of 2 or 3 do not satisfy the word both.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.

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