Question

hat are some other rules that would make this input-output pair true?
input
6
rule
Input Output Arrow
?
Input Output Arrow
output
4
Could be a rule for this input-output pair Could not be a rule for this
input-output pair
Subtract 2.
Write 4.
Divide by 2, then add 1.
If even, subtract 2. If odd, add 5.
Write 6.
Divide by 6, then add 2.

Answer 1

To determine whether the proposed rules could make the input-output pair of 6 leading to an output of 4 true, we can analyze each rule one by one:

1. **Subtract 2.** - This would yield \(6 - 2 = 4\). **Could be a rule for this input-output pair.**

2. **Write 4.** - This simply states to write the number 4, regardless of the input. **Could be a rule for this input-output pair.**

3. **Divide by 2, then add 1.** - Performing this operation: \(\frac{6}{2} + 1 = 3 + 1 = 4\). **Could be a rule for this input-output pair.**

4. **If even, subtract 2. If odd, add 5.** - Since 6 is even, we subtract 2: \(6 - 2 = 4\). **Could be a rule for this input-output pair.**

5. **Write 6.** - This rule suggests writing the number 6 regardless of the input. **Could not be a rule for this input-output pair.** (since the output is 4)

6. **Divide by 6, then add 2.** - Performing this operation: \(\frac{6}{6} + 2 = 1 + 2 = 3\). **Could not be a rule for this input-output pair.** (since the output is 4)

### Summary:
- Could be a rule:
- Subtract 2.
- Write 4.
- Divide by 2, then add 1.
- If even, subtract 2. If odd, add 5.

- Could not be a rule:
- Write 6.
- Divide by 6, then add 2.

These evaluations help clarify which operations or statements align with the input-output transformation defined.