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

Step 2, Step 4, Step 1, Step 3

Answer 1

To prove that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational, we can organize the steps in the correct sequence as follows:

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.

Therefore, the correct order is Step 2, Step 1, Step 4, Step 3. This matches the option Step 2, Step 4, Step 1, Step 3.

To summarize, the reasoning involves first assuming \( t \) is rational, then manipulating the terms to ultimately reach a contradiction.