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.

Answer 1

@amistre64
@jim_thompson5910
@dpaInc
@experimentX

Answer 2

Thanks!

Answer 3

Joshua and Denise's statement contradicts each other; but nobody's accused Joshua, therefore Joshua broke the vase.

Answer 4

http://openstudy.com/users/cbrusoe#/updates/4fb3bab7e4b0556534297dda
she has asked similar questions a lot

Answer 5

No Joshua didn't break the vase you have to use Indirect Proofing so here's a break down to use -
Given:
Nathan: Denise broke the vase.
Joshua: Michelle did it.
Michelle: I did not do it.
Denise: Joshua lied when he said Michelle did it.

Prove: The caretaker was wrong on blaming Denise for the broken vase.
For an Indirect proof, assume that Denise did not break the vase. Assuming she didn't. Nathan's statement that Denise broke the vase is FALSE. Assuming that Denise did not break the vase, Joshua's statement that Michelle did it is TRUE. Now Michelle's statement that I did not do it is FALSE. Finally Denise's statement that Joshua lied when he said Michelle did it is FALSE. Since three of the four given statements contradict the assumption, the assumption is false; therefore, its opposite is true. Denise didn't break the vase.

Answer 6

So really Michelle broke the vase.