Question

Shelly, Susan, and Samantha are all working at an amusement park for the summer. The manager finds out that one of them left the key in the door to the security office. When he asked them who did it, they replied:

Shelly: Susan did it.
Susan: I didn’t do it.
Samantha: Susan did not do it.

The manager concluded that Susan did it because she was accused and was denying it.

Use an indirect proof to show that the manager was wrong and that Susan did not leave the key in the security office door.

Answer 1

HINT: two people said that susan didn't do it.

Answer 2

Begin by assuming that Susan did do it. Then show that that assumption leads to a contradiction of a known fact.

Answer 3

So something like Since two people said that Susan didn't do it and Shelly who was the only one to accuse Susan, must have done it?

Answer 4

Assume that Susan left the key in the security room door.
Given: Susan did not leave the key in the security room door as reported by Samantha.
Therefore the assumption is false and Susan did not leave the key in the security room door and the manager is incorrect.

Answer 5

but is that really an indirect proof or just an assumption?

Answer 6

Do what you want. That is the way you do an indirect proof. Since you have no given facts in the problem just accusations and denials, the entire problem is ridiculous but that is the format of an indirect proof.

Answer 7

Oh ok thanks :) Sorry i had to ask i'm having trouble on this subject.