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

If A₁ = {x : x ∈ ℕ, x is a multiple of both 10 and 15}, what type of set is A₁?

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Answer and explanation

Correct answer: Infinite

A number that is a multiple of both 10 and 15 must be a multiple of their least common multiple. Since lcm(10, 15) = 30, the set is A₁ = {30, 60, 90, 120, ...}. There is no upper bound on x, so new common multiples can always be found by continuing the sequence. Therefore, A₁ is an infinite set.

Tags

setsinfinite setcommon multiplesleast 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

Why is this the correct answer?

A number that is a multiple of both 10 and 15 must be a multiple of their least common multiple. Since lcm(10, 15) = 30, the set is A₁ = {30, 60, 90, 120, ...}. There is no upper bound on x, so new common multiples can always be found by continuing the sequence. Therefore, A₁ is an infinite 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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