What is the roster form of D = {x : x ∈ ℕ, x is a factor of 36, and x is odd}?
Answer and explanation
Correct answer: D = {1, 3, 9}
The governing idea is to apply both restrictions in the definition: a member must be a positive factor of 36 and must be odd. The positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Selecting only the odd factors leaves 1, 3, and 9. Thus D = {1, 3, 9}, so option A is correct. Option B omits the valid factor 1; C includes even 6; D includes 12, which is also even.
Frequently asked questions
What is the correct answer to this question?
D = {1, 3, 9}
Why is this the correct answer?
The governing idea is to apply both restrictions in the definition: a member must be a positive factor of 36 and must be odd. The positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Selecting only the odd factors leaves 1, 3, and 9. Thus D = {1, 3, 9}, so option A is correct. Option B omits the valid factor 1; C includes even 6; D includes 12, which is also even.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
