Let's analyze the question to identify the correct set of possible values for a given condition where [tex]\( n = 3 \)[/tex].
The options provided are:
1. [tex]\( \{0, 1, 2\} \)[/tex]
2. [tex]\( \{0, 1, 2, 3\} \)[/tex]
3. [tex]\( \{-2, -1, 0, 1, 2\} \)[/tex]
4. [tex]\( \{-3, -2, -1, 0, 1, 2, 3\} \)[/tex]
In the context of the problem, we need to determine which set includes all the possible values of [tex]\( /\)[/tex] for [tex]\( n = 3 \)[/tex].
### Detailed Examination of Options:
1. Option 1: [tex]\( \{0, 1, 2\} \)[/tex]:
- This set only includes numbers from [tex]\( 0 \)[/tex] to [tex]\( 2 \)[/tex]. It misses several other potential values.
2. Option 2: [tex]\( \{0, 1, 2, 3\} \)[/tex]:
- This set includes numbers from [tex]\( 0 \)[/tex] to [tex]\( 3 \)[/tex], but it also misses negative values which can be possible.
3. Option 3: [tex]\( \{-2, -1, 0, 1, 2\} \)[/tex]:
- This set includes some negative values and some positive values but does not cover the entire range of possible outcomes as it misses [tex]\( -3 \)[/tex] and [tex]\( 3 \)[/tex].
4. Option 4: [tex]\( \{-3, -2, -1, 0, 1, 2, 3\} \)[/tex]:
- This set includes both negative and positive values as well as zero, covering the entire range from [tex]\( -3 \)[/tex] to [tex]\( 3 \)[/tex].
### Conclusion:
By examining all the provided options, we can conclude that the set which comprehensively includes all the possible values for [tex]\( /\)[/tex] when [tex]\( n = 3 \)[/tex] is the fourth option:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Therefore, the correct set of possible values is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
