To prove that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational, the correct sequence of steps is as follows:
- Step 2: For a contradiction, assume that \( t \) is rational, and write \( r \) and \( t \) as fractions.
- Step 4: Find a common denominator.
- Step 1: Subtract, writing \( s \) as a fraction.
- Step 3: Realize a contradiction.
Thus, the correct sequence is:
D. step 2, step 4, step 1, step 3