What is the roster form of S₁ = {x : x ∈ ℕ, x is a factor of 45 and x + 2 is prime}?
Answer and explanation
Correct answer: S₁ = {1, 3, 5, 9, 15, 45}
The natural-number factors of 45 are 1, 3, 5, 9, 15 and 45. Adding 2 to these values gives 3, 5, 7, 11, 17 and 47, respectively. Every one of these results is prime. Hence every factor of 45 satisfies the second condition as well, so the complete roster form is S₁ = {1, 3, 5, 9, 15, 45}. Option C is incorrect because it omits valid factors.
Frequently asked questions
What is the correct answer to this question?
S₁ = {1, 3, 5, 9, 15, 45}
Why is this the correct answer?
The natural-number factors of 45 are 1, 3, 5, 9, 15 and 45. Adding 2 to these values gives 3, 5, 7, 11, 17 and 47, respectively. Every one of these results is prime. Hence every factor of 45 satisfies the second condition as well, so the complete roster form is S₁ = {1, 3, 5, 9, 15, 45}. Option C is incorrect because it omits valid factors.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
