Answer :
To determine the correct set of possible values of \( I \) for \( n = 3 \), we need to consider the range of integers that span from \(-n\) to \(n\).
When \( n = 3 \), the range of possible values of \( I \) includes all integers from \(-3\) to \(3\). Therefore, we list all the integers within this range:
[tex]\[ -3, -2, -1, 0, 1, 2, 3 \][/tex]
Thus, the correct set of possible values of \( I \) for \( n = 3 \) is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Comparing this with the given choices:
1. \( \{0, 1, 2\} \): This set does not include all integers from \(-3\) to \(3\).
2. \( \{0, 1, 2, 3\} \): This set does not include all negative integers from \(-3\) to \(0\).
3. \( \{-2, -1, 0, 1, 2\} \): This set does not include \(-3\) and \(3\).
4. \( \{-3, -2, -1, 0, 1, 2, 3\} \): This set includes all integers from \(-3\) to \(3\).
The correct set of possible values of \( I \) for \( n = 3 \) is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Therefore, the answer is:
[tex]\[ \boxed{-3, -2, -1, 0, 1, 2, 3} \][/tex]
When \( n = 3 \), the range of possible values of \( I \) includes all integers from \(-3\) to \(3\). Therefore, we list all the integers within this range:
[tex]\[ -3, -2, -1, 0, 1, 2, 3 \][/tex]
Thus, the correct set of possible values of \( I \) for \( n = 3 \) is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Comparing this with the given choices:
1. \( \{0, 1, 2\} \): This set does not include all integers from \(-3\) to \(3\).
2. \( \{0, 1, 2, 3\} \): This set does not include all negative integers from \(-3\) to \(0\).
3. \( \{-2, -1, 0, 1, 2\} \): This set does not include \(-3\) and \(3\).
4. \( \{-3, -2, -1, 0, 1, 2, 3\} \): This set includes all integers from \(-3\) to \(3\).
The correct set of possible values of \( I \) for \( n = 3 \) is:
[tex]\[ \{-3, -2, -1, 0, 1, 2, 3\} \][/tex]
Therefore, the answer is:
[tex]\[ \boxed{-3, -2, -1, 0, 1, 2, 3} \][/tex]
