Nathan, Joshua, Michelle, and Denise were in a room where a porcelain vase was found broken. When an inquiry was conducted by the building caretaker, each made a statement.

Nathan: I did not break the vase.
Joshua: Denise did it.
Michelle: Denise lied when she said Michelle did it.
Denise: Michelle did it.

The caretaker knew that only one statement is not true and concluded that Nathan broke the vase.

Describe in complete sentences the method you use to show that the caretaker made an incorrect conclusion.

Question

Nathan, Joshua, Michelle, and Denise were in a room where a porcelain vase was found broken. When an inquiry was conducted by the building caretaker, each made a statement. 

Nathan: I did not break the vase. 
Joshua: Denise did it. 
Michelle: Denise lied when she said Michelle did it. 
Denise: Michelle did it. 

The caretaker knew that only one statement is not true and concluded that Nathan broke the vase. 

Describe in complete sentences the method you use to show that the caretaker made an incorrect conclusion.

anonymous · Answer

@amistre64

anonymous · Answer

maybe the answer is denise

anonymous · Answer

Well from the given information, Michelle's statement is true, and Denise's statement is false. Joshua's statement is also true. The only logical explanation is that Denise broke the vase, because she was the only one that lied.

anonymous · Answer

But I'm not sure what type of "method" I should use to explain my reasoning.

anonymous · Answer

Denise and Michelle's statements contradict each other

amistre64 · Answer

maybe converses?

-Nathan: I did break the vase. 
-Joshua: Denise did not it. 
-Michelle: Denise told the truth when she said Michelle did not do it. 
-Denise: Michelle did not it.

anonymous · Answer

I think I need to use an indirect proof, or proof by contradiction, or something along those lines.

amistre64 · Answer

i never did get the feel of these types of questions

anonymous · Answer

I'm not sure how to answer it. It's the last question on my practice packet and I'm completely stuck. The only answer I feel that I can give is "Denise's and Michelle's statements contradict each other, so one of them bust be lying. Therefore, Joshua's statement is the truth, Denise broke the vase."

anonymous · Answer

And I guess I can use proof by contradiction as my method.

anonymous · Answer

Given:

Nathan: I did not break the vase. 
Joshua: Denise did it. 
Michelle: Denise lied when she said Michelle did it. 
Denise: Michelle did it. 

Prove: The caretaker's conclusion that Nathan broke the vase was incorrect. 

By using the method of Proof by Contradictions we can conclude that Denise's and Michelle's statements contradict each other, so one of them must be lying. Therefore, Joshua's statement is true, Denise broke the vase. Aside from the using the method of proof by contradiction, it makes logical sense that Denise broke the vase because she was the only person who lied.

anonymous · Answer

Does that sound right?