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

First I would assume the opposite, Michelle did not brake the vase. Since only one statement is not true Denise and Nathan's statement prove that Joshua broke the vase and Michelle's statement is false. Therefore the caretaker's conclusion was incorrect.
This is what I have so far...I'm just not sure if it's right.

Answer 2

@ganeshie8 Hey! ( : Can you help me with this?

Answer 3

Thats a very good try :)

Answer 4

but, in indirect proofs, we need to assume the opposite of WHAT WE NEED TO PROVE

Answer 5

Here we wanto prove caretaker made an incorrect conclusion,
caretaker concluded Michelle broke the vase

you wanto prove what ?

Answer 6

you want to prove : Michelle DID NOT broke the vase

Answer 7

yes

Answer 8

Since we want to prove Michelle DID NOT broke the vase, lets start by assuming the opposite of what we need to prove as TRUE. Lets assume that Michelle DID broke the vase.....

Answer 9

getting ? we need to assume "Michelle broke the vase" and look for contradiciton ok

Answer 10

Ok, so Denise and Nathan's statement contradict that

Answer 11

and michele's

Answer 12

Step 1 : Assume the opposite of what we need to prove :-

Since we want to prove Michelle DID NOT broke the vase, lets start by assuming the opposite of what we need to prove as TRUE. Lets assume that Michelle DID broke the vase

Step 2 : look for contradiction :-
Nathan: Joshua broke the vase. \(FALSE \)
Joshua: Nathan did not do it. \(TRUE \)
Michelle: Joshua lied when he said Nathan did not do it. \(TRUE \)
Denise: Joshua did it. \(FALSE\)

Step 3 : Conclude I want you do this :)

Answer 13

Yes, oly denise and Nathan's statements are contradiction,
but we did get a contradiction. So the assumption must be wrong.. can u conclude ?

Answer 14

Since Denise and Nathan's statements contradict the assumption, Michelle broke the vase, the assumption is wrong?

Answer 15

Yup ! put it something like below :-

Since Denise and Nathan's statements are contradicting, Our initial assumption that Michelle broke the vase, must be FALSE. So, Michelle DID NOT broke the vase, and hence the caretaker was proven wrong.

Answer 16

Thanks ganeshie! C:

Answer 17

np :)