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

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

anonymous · Answer

Nathan is claiming that Denise broke the vase. If this were true, then Nathan, Michelle and Denise would all have true statements, thus there are three true statements. If it is "known" that there are only two true statements, this cannot be so.