If A = {x : x ∈ ℕ, x is a prime factor of 24}, which set is A?
Answer and explanation
Correct answer: {2, 3}
The prime factorisation of 24 is 24 = 2 × 2 × 2 × 3 = 2³ × 3. The prime factors are therefore 2 and 3. A set records membership, not repeated occurrences, so 2 is written only once even though it appears three times in the factorisation. Neither 1 nor 24 is a prime factor, and 8 is not prime. Hence A = {2, 3}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
{2, 3}
Why is this the correct answer?
The prime factorisation of 24 is 24 = 2 × 2 × 2 × 3 = 2³ × 3. The prime factors are therefore 2 and 3. A set records membership, not repeated occurrences, so 2 is written only once even though it appears three times in the factorisation. Neither 1 nor 24 is a prime factor, and 8 is not prime. Hence A = {2, 3}, making option A 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.
