To determine which set of numbers gives the correct possible values of [tex]\( I \)[/tex] for [tex]\( n = 3 \)[/tex], we need to consider the range of numbers from [tex]\(-n\)[/tex] to [tex]\( n \)[/tex].
Given [tex]\( n = 3 \)[/tex]:
- The range from [tex]\(-n\)[/tex] to [tex]\( n \)[/tex] is [tex]\(-3\)[/tex] to [tex]\( 3 \)[/tex].
- This means the possible values of [tex]\( I \)[/tex] should include all integers starting from [tex]\(-3\)[/tex] up to [tex]\( 3 \)[/tex].
Now let's examine each set of numbers to see which one fits within this range:
1. [tex]\( \{0, 1, 2\} \)[/tex] includes numbers from 0 to 2 but does not cover the entire range from [tex]\(-3\)[/tex] to 3.
2. [tex]\( \{0, 1, 2, 3\} \)[/tex] includes numbers from 0 to 3 but again, does not cover the entire range from [tex]\(-3\)[/tex] to 3.
3. [tex]\( \{-2, -1, 0, 1, 2\} \)[/tex] includes numbers from [tex]\(-2\)[/tex] to 2 but does not cover the entire range from [tex]\(-3\)[/tex] to 3.
4. [tex]\( \{-3, -2, -1, 0, 1, 2, 3\} \)[/tex] includes all numbers from [tex]\(-3\)[/tex] to 3, matching the required range perfectly.
Therefore, the correct set of numbers that gives the possible values of [tex]\( I \)[/tex] for [tex]\( n = 3 \)[/tex] is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
