hat are some other rules that would make this input-output pair true?

Question

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.