Question

Someone please help me! Shelly, Jess, and Andrea 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: Andrea did it.
Jess: Shelly did not do it.
Andrea: I didn’t do it.

The manager believed Jess. Use an indirect proof to show that Shelly did not leave the key in the security office door.

Hint: Begin by assuming Shelly did leave the key in the door.

Answer 1

Please help me!

Answer 2

It states that

"Begin by assuming Shelly did leave the key in the door"

So let's do so

Answer 3

If we assume that, then Shelly's statement of "Andrea did it" is a lie. It's a lie because we're assuming that Shelly did it (and not Andrea).


Also, this assumption would mean that Jess is lying too. But why would we have two liars when there's only one culprit (assuming no conspiracy is going on)?


So because of this assumption, we have a contradiction. To avoid the contradiction, the opposite must be true.


So this means that Shelly didn't do it. Therefore, Jess is correct.

Answer 4

Note: this doesn't prove that Shelly is correct, it just proves that she didn't do it

Answer 5

Thank you!!!!

Answer 6

you're welcome