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
Subtract 3, then divide by 5.
If odd, subtract 9. If even, write 3.

Answer 1

To determine which rules would make the input-output pair (12 as input and 7 as output) true, we need to analyze the proposed rules.

1. Subtract 3, then divide by 5:

   • Start with the input, 12.
   • Subtract 3: 12 - 3 = 9.
   • Now, divide by 5: 9 ÷ 5 = 1.8, which does not equal 7.
   • Conclusion: This rule could not be a rule for this input-output pair.

2. If odd, subtract 9. If even, write 3:

   • Here, we need to check if 12 (input) is even or odd.
   • 12 is an even number. According to the rule, if the input is even, we "write 3." Since the output is 7, this rule does not apply.
   • Conclusion: This rule could not be a rule for this input-output pair.

Based on this analysis, both proposed rules do not yield the output of 7 when the input is 12. Therefore, they cannot be true for this input-output pair.