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.

Answer 1

You can set up a logic table to outline the consequences of each statement being true or false and what that would imply.

Answer 2

its denise how broke it right?

Answer 3

who*

Answer 4

If we assume that only one person is lying, then that would be a logical conclusion.

Answer 5

Otherwise, if we say Nathan did it, then that would mean both Joshua and Denise were lying, and so on.

Answer 6

i still dont understand.. i think it is either michelle of denise who did it

Answer 7

If Michelle did it, then she would be lying when she said that Denise was lying about Michelle doing it, but Joshua said Denise did it, so that would mean that both Michelle and Joshua were lying.
This conclusion rests on the assumption that only one of them is lying.

Answer 8

http://openstudy.com/study#/updates/4fbd6653e4b0c25bf8fbbea1

Answer 9

@hartnn similar setup, but different statements.

Answer 10

In that other situation, if Nathan did it, then both Joshua and Denise are also both lying.
Anyway, that's irrelevant to this problem.

Answer 11

im still confused.

Answer 12

why would it be nathan now

Answer 13

I'm confused too. i don't know what @hartnn is talking about. He brought up a similar-sounding problem from another thread and is making illogical statements about it. It has nothing to do with the one you posted here.

Answer 14

hmm...sorry.

Answer 15

With only four statements to look at, it's easy enough to go through each scenario one at a time and ask the following question: "If this person did it, then how many other people must be lying?"
If we accept that the caretaker is correct about there only being one false statement, then you know you have it right when you only count one possible false statement in your checking of each scenario.

Answer 16

so denise made the false statement

Answer 17

joshua said that denise did and and michelle is basically saying she didnt do it .. is that right?

Answer 18

@ganeshie8 @experimentX do you guys understand any of this?

Answer 19

you should prove this by "proof by contradiction"

Answer 20

begin by assuming the opposite of what u need to prove.

Answer 21

since, you wanto
... .show that the caretaker made an incorrect conclusion.

Answer 22

assume the opposite is true and start :

assume : caretaker made a correct conclusion.

Answer 23

I'm tired of this question ... try to google
https://www.google.com/search?q=Nathan%3A+I+did+not+break+the+vase.++Joshua%3A+Denise+did+it.++Michelle%3A+Denise+lied+when+she+said+Michelle+did+it.++Denise%3A+Michelle+did+it.&rlz=1C1ASUT_enNP447NP447&sugexp=chrome,mod=10&sourceid=chrome&ie=UTF-8
this question is a FAQ

Answer 24

caretaker concluded that Nathan broke tha case,

Nathan: I did not break the vase. (FALSE)
Joshua: Denise did it. (FALSE)
Michelle: Denise lied when she said Michelle did it. (TRUE)
Denise: Michelle did it. (FALSE)

since 3 out of four given statements are FALSE and contradicting the caretaker's conclusion. caretaker made an incorrect conclusion.

Answer 25

see if that makes sense to u

Answer 26

and u are correct that denise made a false statement

Answer 27

only that makes other three statements true.

Answer 28

(Which is what I said over 20 comments ago..) LOL