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

The manager concluded that Shelly left the key in the security room’s door.

Use an indirect proof to show that the manager was wrong and that Shelly did not leave the key in the security room’s door.

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: Samantha did it. 
Susan: Shelly did not do it. 
Samantha: I didn’t do it. 

The manager concluded that Shelly left the key in the security room’s door. 

Use an indirect proof to show that the manager was wrong and that Shelly did not leave the key in the security room’s door.

anonymous · Answer

@satellite73 or @Mertsj can one of u  guys help me with this

mertsj · Answer

Did you begin by assuming that Shelly did not leave the key in the door?

anonymous · Answer

@Mertsj yes I did

mertsj · Answer

Did you show that the assumption does not lead to a contradiction of a known fact?

anonymous · Answer

@Mertsj yes, because we have not proven that she is guilty yet

mertsj · Answer

None of the three statements contradicts our assumption that Shelly did not leave the key in the door.

mertsj · Answer

So our assumption is correct, the manager is wrong and Shelly did not leave the key in the door.

anonymous · Answer

ok thx @Mertsj

mertsj · Answer

yw