Certainly! Let's write the given set using the roster (listing) method.
The given set is defined as [tex]\(\{x \in \mathbb{N} \mid 4 \leq x < 10\}\)[/tex], where [tex]\(\mathbb{N}\)[/tex] represents the set of natural numbers. This means we are looking for all natural numbers [tex]\(x\)[/tex] that satisfy [tex]\(4 \leq x < 10\)[/tex].
1. We start from the smallest number that meets the condition: [tex]\(4\)[/tex].
2. We list each subsequent natural number that satisfies [tex]\(4 \leq x < 10\)[/tex]:
- Next number is [tex]\(5\)[/tex].
- Followed by: [tex]\(6\)[/tex].
- Then: [tex]\(7\)[/tex].
- Next: [tex]\(8\)[/tex].
- Finally: [tex]\(9\)[/tex].
3. We stop at [tex]\(9\)[/tex] because the condition [tex]\(x < 10\)[/tex] excludes [tex]\(10\)[/tex] and any higher numbers.
Therefore, the set expressed using the roster method is:
[tex]\[ \{4,5,6,7,8,9\} \][/tex]
