What is the roster form of X = {x : x ∈ ℕ, x ≤ 10, and x is neither prime nor composite}?
Answer and explanation
Correct answer: X = {1}
The governing concept is classification of natural numbers into prime, composite, or neither. From 1 through 10, the primes are 2, 3, 5, and 7; the composites are 4, 6, 8, 9, and 10. The number 1 has only one positive divisor, so it is neither prime nor composite. Under the usual school convention ℕ = {1, 2, 3, …}, X = {1}; therefore option A is correct. Option B incorrectly includes 0, while C and D do not satisfy the condition.
Frequently asked questions
What is the correct answer to this question?
X = {1}
Why is this the correct answer?
The governing concept is classification of natural numbers into prime, composite, or neither. From 1 through 10, the primes are 2, 3, 5, and 7; the composites are 4, 6, 8, 9, and 10. The number 1 has only one positive divisor, so it is neither prime nor composite. Under the usual school convention ℕ = {1, 2, 3, …}, X = {1}; therefore option A is correct. Option B incorrectly includes 0, while C and D do not satisfy the condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
