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. i need help im really confused on how to do this ?

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.  i need help im really confused on how to do this ?

anonymous · Answer

this is math?

anonymous · Answer

what type of method do you need?

anonymous · Answer

an indirect proof but i dont know how to

anonymous · Answer

You first make assumption that Nathan's statement is the lie and other statements are correct, you will see the statements contradict each other so they cannot be true. Then assume Joshua lied and the other statements are true, but again Denise and Michelle's statements canot be true at the same time. Now assume Michelle lied, then Joshua nd Denise statements cant be true at the same time. Only when we assume Denise was lying, all other statments are true and donot contradict each other. Hence it is Denise who broke the vase, not Nathan