Put the steps to the proof that the sum t = r + 8 is irrational if r is a rational and 8 is rational in the correct sequence.

Question

Put the steps to the proof that the sum t = r + 8 is irrational if r is a rational and 8 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)
• Step 4, Step 2, Step 1, Step 3
• Step 1, Step 3, Step 2, Step 4
• Step 2, Step 4, Step 1, Step 3
• Step 3, Step 4, Step 2, Step 1

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1 answer
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Answer 1

Bot GPT 4-o mini answered
2 months ago

To prove that the sum \( t = r + 8 \) is irrational if \( r \) is rational and 8 is rational, the correct sequence of steps is:

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

So, the correct answer is:
• Step 2, Step 4, Step 1, Step 3