Match the set $\{1, 2, 3, 6, 9, 18\}$ (roster form) with the correct set-builder form.
A$\{x : x \text{ is a positive integer and is a divisor of } 18\}$
B$\{x : x \text{ is an integer and } x^{2} - 9 = 0\}$
C$\{x : x \text{ is a multiple of } 3 \text{ less than } 20\}$
D$\{x : x \text{ is a prime number less than } 20\}$
Answer & Solution
Correct answer: A. $\{x : x \text{ is a positive integer and is a divisor of } 18\}$
The positive divisors of $18$ are exactly $\{1, 2, 3, 6, 9, 18\}$ ($18 = 2 \cdot 3^{2}$, so divisors are products of $2^{i} \cdot 3^{j}$ with $i \in \{0, 1\}$, $j \in \{0, 1, 2\}$, giving $6$ divisors).
- **B** gives $\{3, -3\}$, a different set.
- **C** gives $\{3, 6, 9, 12, 15, 18\}$ — different.
- **D** gives $\{2, 3, 5, 7, 11, 13, 17, 19\}$ — different.
Only **A** matches. This is from NCERT Class 11, Example 5.
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