To determine the correct set of possible values for [tex]\( I \)[/tex] when [tex]\( n = 3 \)[/tex], let's carefully analyze the given parameters and the question.
We are looking for a set of values that [tex]\( I \)[/tex] can take when the value of [tex]\( n \)[/tex] is 3. Generally, when we talk about indices or certain sequences starting from zero, the values [tex]\( I \)[/tex] can take range from 0 to [tex]\( n \)[/tex].
For [tex]\( n = 3 \)[/tex], the values [tex]\( I \)[/tex] can take would start from 0 and go up to 3. So let’s enumerate the values between 0 and [tex]\( n \)[/tex]:
- When [tex]\( n = 3 \)[/tex], the possible integer values for [tex]\( I \)[/tex] are: 0, 1, 2, and 3.
Now, we compare this set of values to the given options:
1. [tex]\( \{0, 1, 2\} \)[/tex] - This set includes values from 0 to 2, which doesn't cover all possible indices up to 3.
2. [tex]\( \{0, 1, 2, 3\} \)[/tex] - This set includes values from 0 to 3, which perfectly covers the range of possible values for [tex]\( I \)[/tex].
3. [tex]\( \{-2, -1, 0, 1, 2\} \)[/tex] - This set includes negative values and stops at 2, which does not cover the range required for [tex]\( n = 3 \)[/tex].
4. [tex]\( \{-3, -2, -1, 0, 1, 2, 3\} \)[/tex] - This set includes a wider range of values, including negatives, which is beyond the necessary range.
Based on this analysis, the correct set of numbers that gives all possible values of [tex]\( I \)[/tex] for [tex]\( n = 3 \)[/tex] is:
[tex]\[ \{0, 1, 2, 3\} \][/tex]
So the answer is [tex]\( \{0, 1, 2, 3\} \)[/tex].
