Question

Amanda did the following proof in her logic class. Which step in the indirect proof did she do incorrectly?

Prove: 9 is divisible by 3.

Step 1: Assume that 9 is divisible by three.
Step 2: 3 times 3 equals nine. 9 divided by three is three.
Step 3: 9 is divisible by 3.
Answer
Step 2
Step 1
Step 3
Steps 2 and 3

Answer 1

pleASE ANSWER THIS!!

Answer 2

MERTSJ

Answer 3

ANY1 PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 4

Step 2 is incorrect. Because in step 1 she assume 9 is divisible by 3. So in step 2 she should have affirmed that assumption by taking 9 and divide it by 3. Then multiplying 3 by 3 to get 9 again.

SO the correct way would be
Step 2:9 divided by 3 is 3, 3 times 3 equals 9.

Answer 5

TY

Answer 6

Think about it this way...
Prove that 1=2.
Step 1: Assume that 1=2.
Step 2: 1*0=0, and 2*0=0.
Step 3: Thus, 1=2.

What is the incorrect step there?

Answer 7

Step 2 is NOT the correct answer, guys.

Answer 8

STEP 3

Answer 9

IT IS 3

Answer 10

Hmm...well technically yes in my example, though not for yours...

Answer 11

SO HOW DO IDO MINE

Answer 12

Note how it is blatantly WRONG to do step 1. You are starting by assuming something that is false is in fact true! You can't do that! To prove something you need to take only TRUE statements, and then derive the statement you want to prove.

Answer 13

OK

Answer 14

SO WHAT SHALL I DO

Answer 15

Hmm i thought about that also. But in mathematical induction, isn't it okay to assume the truth of the equation first?
Cause the question also mentions a indirect proof, so i sort of think of a "working-backwards-kinda proof"

Answer 16

IS IT STEP 1?

Answer 17

However, in induction, you have a base step, so you know for at least SOME case it works, so you're not working completely arbitrarily.

Answer 18

AHH OK

Answer 19

Yes i agree with yakeyglee now. The incorrect step is step 1.

It should be replaced with the following:

Step 1: Assume that 9 is not divisible by 3

Answer 20

TY

Answer 21

Yes, that would be a proof by contradiction, which is logically valid. :)

Answer 22

You need to prove it via 'reductio ad absurdum'; step 1 is incorrect..