Question

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

Answer 1

The correct sequence for the proof that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational 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.

Thus, the complete correct response is: Step 2, Step 4, Step 1, Step 3.