To determine which set of numbers gives the correct possible values of 1 for [tex]\( n = 2 \)[/tex], let's evaluate each given set of numbers:
### Step-by-Step Evaluation:
1. Set 1: [tex]\(\{0\}\)[/tex]
- Only contains the number 0.
- This set does not address other potential values, and it's incomplete relative to the given options.
2. Set 2: [tex]\(\{0, 1\}\)[/tex]
- Contains the numbers 0 and 1.
- While it includes 1, it might miss other valid numbers.
3. Set 3: [tex]\(\{0, 1, 2\}\)[/tex]
- Contains the numbers 0, 1, and 2.
- 1 is within this set, and it includes other possible values up to [tex]\( n = 2 \)[/tex].
4. Set 4: [tex]\(\{0, 1, 2, 3\}\)[/tex]
- Contains the numbers 0, 1, 2, and 3.
- This set seems larger than necessary since [tex]\( n \)[/tex] is just 2.
### Conclusion:
By examining these sets, Set 3: [tex]\(\{0, 1, 2\}\)[/tex] efficiently captures the correct possible values within the range of 0 to [tex]\( n = 2 \)[/tex]. It includes:
- 0 (lower bound)
- 1 (the value of interest)
- 2 (the given value for [tex]\( n \)[/tex])
Thus, the set [tex]\(\{0, 1, 2\}\)[/tex] correctly represents the possible values of 1 for [tex]\( n = 2 \)[/tex].
