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Class 10MathematicsSetsSets and their representationsEasyLevel 3

If F₁ = {x : x ∈ ℕ, x has exactly two distinct positive factors and x < 15}, what is F₁?

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Answer and explanation

Correct answer: F₁ = {2, 3, 5, 7, 11, 13}

A natural number has exactly two distinct positive factors precisely when it is prime: the number itself and 1. The prime numbers less than 15 are 2, 3, 5, 7, 11, and 13. The number 1 is not prime because it has only one positive factor, namely 1. Hence the required set is option B.

Tags

setsprime numbersfactorsnatural numbersroster formSets and their representationsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

F₁ = {2, 3, 5, 7, 11, 13}

Why is this the correct answer?

A natural number has exactly two distinct positive factors precisely when it is prime: the number itself and 1. The prime numbers less than 15 are 2, 3, 5, 7, 11, and 13. The number 1 is not prime because it has only one positive factor, namely 1. Hence the required set is option B.

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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