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

If Z = {x : x ∈ ℕ, x is divisible by both 2 and 3, and x < 20}, what type of set is Z?

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Answer and explanation

Correct answer: Finite set

Numbers divisible by both 2 and 3 are multiples of 6. The positive multiples of 6 that are less than 20 are 6, 12, and 18. There are only three members because the condition x < 20 gives an upper bound. Hence Z is a finite set, even though the unrestricted set of multiples of 6 is infinite.

Tags

setsfinite setdivisibilitybounded setThe 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?

Finite set

Why is this the correct answer?

Numbers divisible by both 2 and 3 are multiples of 6. The positive multiples of 6 that are less than 20 are 6, 12, and 18. There are only three members because the condition x < 20 gives an upper bound. Hence Z is a finite set, even though the unrestricted set of multiples of 6 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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