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Express the set in roster form.
[tex]\[ B = \{x \mid x \in \mathbb{N} \text{ and } x \text{ is a multiple of 6}\} \][/tex]

Choose the correct answer below:
A. [tex]\[ B = \{6\} \][/tex]
B. [tex]\[ B = \{6, 12, 18, 24, \ldots, 600\} \][/tex]
C. [tex]\[ B = \{6, 12, 18, 24, \ldots\} \][/tex]
D. [tex]\[ B = \{12, 18, 24, 30, \ldots\} \][/tex]
E. [tex]\[ B = \{12, 18, 24, 30\} \][/tex]
F. [tex]\[ B = \{6, 12, 18, 24\} \][/tex]
G. [tex]\[ B = \varnothing \][/tex]

Sagot :

GinnyAnswer
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]
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