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.

PLEASE HELP ME!

Answer 1

By what they said, we can say that:
\[\Large {\cancel{Shelly} \cancel {Samantha} Susan}\]
Susan is the only one left. Susan was the one who did it.

Answer 2

Hmm . . . well, I don't remember much about indirect proofs, but here goes!

If Shelly says that Samantha did it, then we have to find out if Samantha did it.
If Samantha says that she didn't do it, then Samantha didn't do it.
So, we can conclude that Samantha didn't do it.
Let's looks at Susan: If Susan says that Shelly didn't do it, then Shelly didn't do it.
If both Shelly and Samantha didn't do it, then Susan did it.
So, based upon this indirect proof, Shelly didn't do it, and Susan did leave the key in the security room's door.

Hope this helps! :)

Answer 3

is that the way it would be used in an indirect proof?

Answer 4

oh thank you lyra!

Answer 5

I'm not sure if this is a correctly-worded indirect proof, though. I do remember that you have to have "if . . . then" in the statement.

Answer 6

oh. well all i need an outlie, i just couldn't figure out the actual problem lol. but i can put it into a actual proof now. thanks :)

Answer 7

outline*

Answer 8

You're very welcome! :) Good luck on your assignment!