Question

Check? Indirect proofs
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 Andrea. Use an indirect proof to show that Andrea did not leave the key in the security office door.

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

Answer 1

@SmoothMath @dpaInc @Calcmathlete

Answer 2

My answer:
Assume Andrea did leave the key in the door. Shelly's statement that Andrea left the key in the door is true. Jess's statement that Shelly did not do it is true. If Andrea did it, then Shelly couldn't have done it. Andrea's statement that she did not leave the key in the door is false. Andrea did leave the key in the door.

Answer 3

Andrea is a good girl. This really doesn't seem like her at all.

Answer 4

LOL ^

Answer 5

@SmoothMath So would my answer be right? i think i did it how it is supposed to be. im just confused all this whole proof think :p

Answer 6

Honestly, I don't like the problem. It seems to me that you need more information to be able to write a proof. Perhaps they are telling you that 1 person is lying at most?

Answer 7

Or wait. I don't know. There's just not enough information here to write a proof. You can't consider witness testimony to be proof, especially if you have conflicting witnesses.

Answer 8

That's what im saying. If i posted a picture of one of the example that they give me do you think you'd be able to see?

Answer 9

I'm interested in seeing their example, yeah.

Answer 10

Given:

Kelly: Meredith forgot the map.
Meredith: Kelly did not forget the map.
Mandy: Meredith lied when she said that Kelly did not forget the map.
Angela: Meredith forgot it.
Prove: Mandy did not forget the map.

For an indirect proof, assume that Mandy did forget the map.

Indirect Two-column Proof Statement Justification
Mandy forgot the map. Assumption of the opposite conclusion.
Kelly’s statement that Meredith forgot the map is FALSE. || If Mandy forgot the map, then Meredith could not have forgotten it.
Meredith’s statement that Kelly did not forget the map is TRUE. || If Mandy forgot the map, then Kelly did not.
Mandy’s statement that Meredith lied when she said that Kelly did not forget the map is FALSE. || If Meredith lied when she said that Kelly did not forget the map, then that would imply that Kelly forgot the map. But, if Mandy forgot the map, then Kelly could not have forgotten it.
Angela’s statement that Meredith forgot it is FALSE. || If Meredith forgot the map, then Mandy could not have been the one who forgot it. And according to the assumption, she did forget the map.

Since three of the four given statements contradict the assumption, the assumption is false. Because the assumption has been proven false, its opposite must be true. Remember, the opposite of the assumption is what you’re trying to prove since you negated the prove statement as the first step.

Prove statement → Negation of prove statement → Opposite of negation = original prove statement

Therefore, Mandy did not forget the map.

Answer 11

Assumption: Proof should be based on evidence, not guessing whether or not someone is lying.
Conclusion: Both of these questions are effing stupid.

Answer 12

Exactly what i dont understand. so do you think my answer is right based on the example.

Answer 13

Their example proof deems to be RELYING on the assumption that 3 people could not be lying.

That makes me initially think that in this problem, you need more information, and that information would be a statement about how many people could be lying.

So, we can look at how many people are lying depending on who may have done it.
If Andrea did it: Andrea is the only one lying.
If Shelly did it: 2 people lying.
If Jess did it: Shelly is the only one lying.

Answer 14

This is so stupid -.- . i agree, they shouldve given more information. ill call my teacher and see what she has to say. thanks so much for the help (: