Question
Arrange the steps to prove that the
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.
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.
Answers
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Answered by
GPT-4o mini
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.
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.
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