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

If C₁ = {x : x ∈ ℕ and x is a factor of both 12 and 18}, what is C₁?

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Answer and explanation

Correct answer: C₁ = {1, 2, 3, 6}

The positive factors of 12 are 1, 2, 3, 4, 6, and 12. The positive factors of 18 are 1, 2, 3, 6, 9, and 18. The elements common to both lists are therefore 1, 2, 3, and 6, so C₁ = {1, 2, 3, 6}. Because a fixed natural number has only finitely many factors, this is a finite set.

Tags

setsfinite setcommon factorsnatural numbersThe 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?

C₁ = {1, 2, 3, 6}

Why is this the correct answer?

The positive factors of 12 are 1, 2, 3, 4, 6, and 12. The positive factors of 18 are 1, 2, 3, 6, 9, and 18. The elements common to both lists are therefore 1, 2, 3, and 6, so C₁ = {1, 2, 3, 6}. Because a fixed natural number has only finitely many factors, this is a finite 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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