Which is the correct roster form of D={x:x is a positive divisor of 12}?
Answer and explanation
Correct answer: D={1,2,3,4,6,12}
The governing concept is the roster form of a set and the meaning of a positive divisor. A positive divisor of 12 must be a positive integer that divides 12 exactly, leaving remainder zero. The factor pairs of 12 are 1×12, 2×6, and 3×4. Therefore, collecting one number from each pair and including every distinct factor gives 1, 2, 3, 4, 6, and 12. Hence option A is correct. Option B omits 1 and 12, so it is incomplete. Option C incorrectly includes 8, because 12÷8 is not an integer. Option D includes 0, but division by zero is undefined and zero cannot be a divisor. The listed elements in A are all positive and each divides 12 exactly.
Frequently asked questions
What is the correct answer to this question?
D={1,2,3,4,6,12}
Why is this the correct answer?
The governing concept is the roster form of a set and the meaning of a positive divisor. A positive divisor of 12 must be a positive integer that divides 12 exactly, leaving remainder zero. The factor pairs of 12 are 1×12, 2×6, and 3×4. Therefore, collecting one number from each pair and including every distinct factor gives 1, 2, 3, 4, 6, and 12. Hence option A is correct. Option B omits 1 and 12, so it is incomplete. Option C incorrectly includes 8, because 12÷8 is not an integer. Option D includes 0, but division by zero is undefined and zero cannot be a divisor. The listed elements in A are all positive and each divides 12 exactly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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