To prove that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational, you can arrange the steps as follows:
- Assume for contradiction that t is rational.
- Write r and s in fractional form.
- Find a common denominator.
- Realize a contradiction.
This order effectively follows the logical process of a proof by contradiction. Starting with the assumption that \( t \) is rational allows you to manipulate \( r \) and \( s \) and ultimately derive a contradiction, proving that \( t \) must be irrational.