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. show your reasoning

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

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

Step 3, Step 4, Step 2, Step 1

1 answer

Step 1, Step 2, Step 4, Step 3

The correct sequence of steps is:
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 4: Find a common denominator.
Step 3: Realize a contradiction.

Step 1 is necessary to simplify the expression of t by writing s as a fraction.
Step 2 involves assuming that t is rational, which allows us to write both r and t as fractions.
Step 4 is necessary to find a common denominator so that we can add r and s as fractions.
Step 3 is where the contradiction is realized, which leads to the conclusion that t must be irrational.