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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 6

What type of set is {x ∈ ℕ : x is prime and x divides 1}?

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Answer and explanation

Correct answer: Empty set

The only natural number that divides 1 is 1 itself. However, 1 is not prime because a prime number must have exactly two distinct positive divisors, namely 1 and itself. Therefore, no natural number satisfies both conditions simultaneously. The set has no elements and is consequently the empty set.

Tags

setsempty setprime numbersdivisibilityThe 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?

Empty set

Why is this the correct answer?

The only natural number that divides 1 is 1 itself. However, 1 is not prime because a prime number must have exactly two distinct positive divisors, namely 1 and itself. Therefore, no natural number satisfies both conditions simultaneously. The set has no elements and is consequently the empty 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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