Question

Which rules would make this input-output pair true?
input
12
rule
Input Output Arrow
?
Input Output Arrow
output
7
Could be a rule for this input-output pair Could not be a rule for this input-output pair
Divide by 6.
Add 2, then divide by 2.
Subtract 5.
Divide by 2, then add 1.

Answer 1

Let's analyze the input-output pair (12 -> 7) using the potential rules provided.

1. **Divide by 6**:
- \( 12 \div 6 = 2 \)
- Output is 2.
- **Could not be a rule**.

2. **Add 2, then divide by 2**:
- \( (12 + 2) \div 2 = 14 \div 2 = 7 \)
- Output is 7.
- **Could be a rule**.

3. **Subtract 5**:
- \( 12 - 5 = 7 \)
- Output is 7.
- **Could be a rule**.

4. **Divide by 2, then add 1**:
- \( (12 \div 2) + 1 = 6 + 1 = 7 \)
- Output is 7.
- **Could be a rule**.

Based on this analysis:

- **Could be a rule for this input-output pair**:
- Add 2, then divide by 2.
- Subtract 5.
- Divide by 2, then add 1.

- **Could not be a rule for this input-output pair**:
- Divide by 6.