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

If B₁ = {x : x ∈ ℕ, x is a multiple of both 10 and 15, and x < 100}, how many elements are in B₁?

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Answer and explanation

Correct answer: 3

The least common multiple of 10 and 15 is 30, so every common multiple is a multiple of 30. The positive multiples of 30 that are less than 100 are 30, 60, and 90. The next multiple, 120, is not less than 100. Thus B₁ = {30, 60, 90}, and its cardinality is 3, so option B is correct.

Tags

setsfinite setcommon multiplescardinalityThe 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?

3

Why is this the correct answer?

The least common multiple of 10 and 15 is 30, so every common multiple is a multiple of 30. The positive multiples of 30 that are less than 100 are 30, 60, and 90. The next multiple, 120, is not less than 100. Thus B₁ = {30, 60, 90}, and its cardinality is 3, so option B is correct.

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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