Arrange the steps to prove that the

Question

sum t = r + s is irrational if r is rational and s is irrational.

1. Assume for contradiction that t is rational.
2. Write r and s in fractional form.
3. Find a common denominator.
4. Realize a contradiction.

Answer 1

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:

1. Assume for contradiction that t is rational.
2. Write r and s in fractional form.
3. Find a common denominator.
4. 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.