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

If A = {x ∈ ℕ : x is prime and x divides 84}, what is A equal to?

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Answer and explanation

Correct answer: {2, 3, 7}

Factor 84 into primes: 84 = 2² × 3 × 7. Its positive divisors include 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84, but the question asks only for prime divisors. The prime divisors are therefore 2, 3, and 7, so A = {2, 3, 7}. The number 1 is not prime, and 4 is composite, so neither belongs in A.

Tags

setsfinite-setprime-factorsdivisorsThe 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, 3, 7}

Why is this the correct answer?

Factor 84 into primes: 84 = 2² × 3 × 7. Its positive divisors include 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84, but the question asks only for prime divisors. The prime divisors are therefore 2, 3, and 7, so A = {2, 3, 7}. The number 1 is not prime, and 4 is composite, so neither belongs in 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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