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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)
Responses

Step 1, Step 3, Step 2, Step 4
Step 1, Step 3, Step 2, Step 4

Step 2, Step 4, Step 1, Step 3
Step 2, Step 4, Step 1, Step 3

Step 4, Step 2, Step 1, Step 3
Step 4, Step 2, Step 1, Step 3

Step 3, Step 4, Step 2, Step 1

1 answer

To prove that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is rational, the steps should be arranged in a logical sequence. The correct sequence 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 order is:

Step 2, Step 4, Step 1, Step 3