Put the steps to the proof that the sum t=r+s is irrational if r is a rational and s is rational in the correct sequence.

Question

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

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

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

Step 1, Step 3, Step 2, Step 4

Answer 1

The correct sequence of the steps to prove that the sum \( t = r + s \) is irrational if both \( r \) and \( s \) are irrational can be identified as follows:

1. Step 2: For a contradiction, assume that \( t \) is rational, and write \( r \) and \( t \) as fractions.

2. Step 4: Find a common denominator.

3. Step 1: Subtract, writing \( s \) as a fraction.

4. Step 3: Realize a contradiction.

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