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: Joshua broke the vase.
Joshua: Nathan did not do it.
Michelle: Joshua lied when he said Nathan did not do it.
Denise: Joshua did it.

The caretaker knew that only one statement is not true and concluded that Michelle 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: Joshua broke the vase. 
Joshua: Nathan did not do it. 
Michelle: Joshua lied when he said Nathan did not do it. 
Denise: Joshua did it. 

The caretaker knew that only one statement is not true and concluded that Michelle broke the vase. 

Describe in complete sentences the method you use to show that the caretaker made an incorrect conclusion.

anonymous · Answer

If we start with the assumption that only one statement in the argument can be false and we start with Nathan's statement, we have an accusation of Joshua breaking the vase. Proceeding to Joshua's statement, we have the assertion that Nathan did not do it which is consistent with the truth-value of Nathan's statement. Next, Michelle's statement accuses Joshua's assertion of being false, and so accusing Nathan which is inconsistent with the truth-value of our argument at this point. As long as the last statement by Denise accusing Joshua is consistent, which it is, we can identify Michelle's statement as the false one but that Joshua is actually guilty.