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)

The correct sequence of steps for the proof that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational would be as follows:

1. **Step 2**: For a contradiction, assume that \( t \) is rational, and write \( r \) and \( t \) as fractions.
2. **Step 1**: Subtract, writing \( s \) as a fraction. Since \( r \) is rational, we can express \( t \) as \( t = r + s \) and hence \( s = t - r \).
3. **Step 4**: Find a common denominator for the fractions representing \( r \) and \( t \).
4. **Step 3**: Realize a contradiction, because if both \( r \) and \( t \) are rational, then \( s \) would also have to be rational, which contradicts the assumption that \( s \) is irrational.

So the correct order is: **2, 1, 4, 3.**

wrong

I apologize for the misunderstanding. Let's carefully sequence the steps to correctly outline the proof that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational:

1. **Step 2**: For a contradiction, assume that \( t \) is rational, and write \( r \) and \( t \) as fractions.
2. **Step 1**: Subtract, writing \( s \) as a fraction.
3. **Step 4**: Find a common denominator.
4. **Step 3**: Realize a contradiction.

So the correct order is: **2, 1, 4, 3.**

Thank you for your patience, and I appreciate your understanding. If you have any more questions or need further clarification, feel free to ask!

NO!!!!!!!!! TAKE YOU RTIME ANSWERING IDIOT

I apologize for the confusion in my previous responses. Let’s carefully go through the proof process step by step again and ensure the sequence is correct.

The goal is to show that if \( r \) is a rational number and \( s \) is an irrational number, then their sum \( t = r + s \) is irrational.

The steps in the correct order are:

1. **Step 2**: For a contradiction, assume that \( t \) is rational, and write \( r \) and \( t \) as fractions.
2. **Step 1**: Subtract, writing \( s \) as a fraction.
3. **Step 4**: Find a common denominator.
4. **Step 3**: Realize a contradiction.

Thus, the correct sequence is: **2, 1, 4, 3.**

Thank you for your patience, and I hope this clarification is helpful. If you have any further questions or concerns, please feel free to ask.