Put the steps to the proof that the sum t=r+s

Question

is irrational if r is a rational and s is rational in the correct sequence.

Step 1. Subtract, writing s as a fraction.

Step 2. For a contradiction, assume that t is rational, and write r and t as fractions.

Step 3. Realize a contradiction.

Step 4. Find a common denominator.

(1 point)
Responses

Step 1, Step 3, Step 2, Step 4
Step 1, Step 3, Step 2, Step 4

Step 3, Step 4, Step 2, Step 1
Step 3, Step 4, Step 2, Step 1

Step 4, Step 2, Step 1, Step 3
Step 4, Step 2, Step 1, Step 3

Step 2, Step 4, Step 1, Step 3

Answer 1

To prove that the sum \( t = r + s \) is irrational if \( r \) is a rational number and \( s \) is rational, the correct sequence of steps is:

1. Step 2: For a contradiction, assume that \( t \) is rational, and write \( r \) and \( t \) as fractions.
2. Step 1: Subtract, writing \( s \) as a fraction.
3. Step 4: Find a common denominator.
4. Step 3: Realize a contradiction.

Thus, the correct order is Step 2, Step 1, Step 4, Step 3.

However, the provided options don't include this exact sequence, and based on standard logic, we can deduce that the closest structured path among available choices would generally follow logical contradiction exploration.

If we were to choose the appropriately matching response based on your provided options, none of the responses perfectly matches the ideal sequence of steps as noted above, but they may intend to illustrate similar logic paths.

Thus pick would need clarification or simpler direct problem restructuring if available options are strictly observed.

In conclusion, a better response might be, Step 2, Step 1, Step 4, Step 3 (based on the sequential logic flow outlined).