What is the roster form of H₁ = {x : x ∈ ℕ, 5 ≤ x ≤ 15, x is composite}?
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Answer and explanation
Correct answer: H₁ = {6, 8, 9, 10, 12, 14, 15}
List the natural numbers from 5 through 15 and classify each one. The composite numbers are 6, 8, 9, 10, 12, 14, and 15 because each has more than two positive factors. The numbers 5, 7, 11, and 13 are prime, so they are excluded. Therefore, option A is the correct roster form.
Frequently asked questions
What is the correct answer to this question?
H₁ = {6, 8, 9, 10, 12, 14, 15}
Why is this the correct answer?
List the natural numbers from 5 through 15 and classify each one. The composite numbers are 6, 8, 9, 10, 12, 14, and 15 because each has more than two positive factors. The numbers 5, 7, 11, and 13 are prime, so they are excluded. Therefore, option A is the correct roster form.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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