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

Let A = {x : x is a prime number and 14 < x < 16}. Which statement about A is correct?

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Answer and explanation

Correct answer: A = ∅

The integers strictly between 14 and 16 contain only 15. However, 15 is not prime because it has divisors 1, 3, 5, and 15; in particular, it is divisible by 3 and 5. Thus no number satisfies both conditions in the set-builder description. Therefore A has no elements and A = ∅.

Tags

setsempty-setprime-numbersset-builder-formThe 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?

A = ∅

Why is this the correct answer?

The integers strictly between 14 and 16 contain only 15. However, 15 is not prime because it has divisors 1, 3, 5, and 15; in particular, it is divisible by 3 and 5. Thus no number satisfies both conditions in the set-builder description. Therefore A has no elements and A = ∅.

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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