Which rules would make this input-output pair true?

Question

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.