Answered

Get the answers you need from a community of experts on IDNLearn.com. Our platform provides accurate, detailed responses to help you navigate any topic with ease.

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 :

GinnyAnsweridn
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]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.