To express the set [tex]\( B = \{x \mid x \in \mathbb{N} \text{ and } x \text{ is a multiple of } 6\} \)[/tex] in roster form, we need to list all the natural numbers that are multiples of 6.
1. Identify the first element: The smallest natural number multiple of 6 is 6 itself.
2. Identify subsequent elements: The next multiple of 6 will be [tex]\( 6 \times 2 = 12 \)[/tex], then [tex]\( 6 \times 3 = 18 \)[/tex], and so on.
3. Determine the form of the set: This pattern continues indefinitely as we only consider multiples of 6 that are natural numbers.
With the steps above, we can now express the set in roster form:
- The elements can clearly be listed as [tex]\( 6, 12, 18, 24, \ldots \)[/tex].
Thus, the correct representation in roster form is:
[tex]\[ B = \{6, 12, 18, 24, \ldots\} \][/tex]
Therefore, the correct answer is:
C. [tex]\( B = \{6, 12, 18, 24, \ldots\} \)[/tex]
