To write Set $B$ using the roster method, we follow these steps:

1. Identify the constraints:

   • Positive two-digit numbers ($10 \leq x \leq 99$).
   • Odd numbers.
   • Less than 46 ($x < 46$).
   • Divisible by 3 ($x \mod 3 = 0$).

2. List the odd two-digit numbers less than 46: $11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45$

3. Filter numbers divisible by 3: $15, 21, 27, 33, 39, 45$

Thus, the set $B$ is: $B = \{15, 21, 27, 33, 39, 45\}$

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Would you like further details or have any questions?

Related Questions:

1. What are the steps for identifying divisibility by 3?
2. How would the solution change if the range extended beyond 46?
3. What if the set included both even and odd numbers?
4. Can you express this set using set-builder notation?
5. How do you find the least common multiple of numbers in this set?

Tip:

When working with constraints, address each condition sequentially to ensure no details are overlooked.