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

If A = {x : x ∈ N, x is a factor of 31}, how many elements are in A?

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Answer and explanation

Correct answer: 2

The number 31 is prime because its only positive divisors are 1 and 31. Consequently, the set of natural-number factors is A = {1, 31}. These are two distinct elements, so the cardinality of A is 2. The number 31 itself is an element, not the number of elements in the set. Therefore, option B is correct.

Tags

setsfinite-setprime-numberThe 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?

2

Why is this the correct answer?

The number 31 is prime because its only positive divisors are 1 and 31. Consequently, the set of natural-number factors is A = {1, 31}. These are two distinct elements, so the cardinality of A is 2. The number 31 itself is an element, not the number of elements in the set. Therefore, 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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