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.

Answer 1

@Mertsj

Answer 2

@SmoothMath

Answer 3

Only one statement is false.
Let us assume that Michelle's statement is true.
Then Joshua's statement is false because Michelle said he lied and Michelle is telling the truth. So if Joshua's statement is false, then Nathan did do it and the caretaker is wrong.

Assume Michelle's statement is false. Then Joshua did NOT lie and Nathan did do it.