Put the steps to the proof that the sum t = r + 8 is irrational if r is a rational and 8 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)
• Step 4, Step 2, Step 1, Step 3
• Step 1, Step 3, Step 2, Step 4
• Step 2, Step 4, Step 1, Step 3
• Step 3, Step 4, Step 2, Step 1

Answer 1

To prove that the sum \( t = r + 8 \) is irrational if \( r \) is rational and 8 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 4: Find a common denominator.
3. Step 1: Subtract, writing \( s \) as a fraction.
4. Step 3: Realize a contradiction.

So, the correct answer is: • Step 2, Step 4, Step 1, Step 3