Which is the correct roster form of C={x:x∈N, 3x≤15}?
Answer and explanation
Correct answer: C={1,2,3,4,5}
The governing concept is conversion from set-builder form to roster form by listing every value that satisfies the stated condition. Here 3x≤15. Since 3 is positive, division by 3 preserves the inequality direction and gives x≤5. The question states x∈N, and the convention used here is N={1,2,3,...}; therefore the eligible natural numbers are 1, 2, 3, 4, and 5. The equality sign is important, so x=5 must be included. Thus C={1,2,3,4,5}, making option B correct. Option A incorrectly includes 0, option C omits 5, and option D lists multiples of 3 rather than values of x.
Frequently asked questions
What is the correct answer to this question?
C={1,2,3,4,5}
Why is this the correct answer?
The governing concept is conversion from set-builder form to roster form by listing every value that satisfies the stated condition. Here 3x≤15. Since 3 is positive, division by 3 preserves the inequality direction and gives x≤5. The question states x∈N, and the convention used here is N={1,2,3,...}; therefore the eligible natural numbers are 1, 2, 3, 4, and 5. The equality sign is important, so x=5 must be included. Thus C={1,2,3,4,5}, making option B correct. Option A incorrectly includes 0, option C omits 5, and option D lists multiples of 3 rather than values of x.
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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