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

May someone please help me???

Answer 2

Michelle: Joshua lied when he said Nathan did not do it.

how does Michelle knows, that Joshua lied ??

Answer 3

either he knows who broke.. in that case he could have said truth..

or else, he himself has broken it.. :D

Answer 4

Ummmm.... I'm looking for a mathematical answer..... I'm sorry, but I have to

Answer 5

lol !!! let me give a try.. u know that truth table ??

Answer 6

Darling, what do you mean when you say "a mathematical answer?" That really gets at what you consider to be the definition of math. Does it have to involve numbers? Variables? Calculation?
Math is a very broad term.

Answer 7

Geometric proofs

Answer 8

@SmoothMath : if u know that truth table, can u show that..

Answer 9

Please help!!!!!

Answer 10

Geometric? You can write a paragraph proof or a two column proof for this, but it has nothing to do with geometry.

Answer 11

Considering the fact that it says "describe in complete sentences," I suppose they would like a paragraph proof.

Answer 12

I'm not particularly into just givin' out answers. How about you show me your attempt, and we can talk about it from there.

Answer 13

Ok, just a moment.......

Answer 14

Basically all of them are blaming Joshua, because Joshua claims Nathan broke the vase, Michelle accused Joshua of lying, Nathan said that Joshua broke the vase, and Denise said that Joshua broke it, so all the evidence points to Joshua. So it wasn't Michelle who broke the vase, but Joshua.

Answer 15

Was I correct? Because I don't think they want it as an explaination.....

Answer 16

I am good at explaining, but bad at listing the specifics.

Answer 17

Well, your explanation is okay, but it kind of leaves things open. You say "All the evidence points to Joshua."

You want to not leave it open like that, but to say DEFINITELY that Joshua did it.
You're told that EXACTLY one of of those 4 people made a false statement. How can you use that fact to say DEFINITELY that Joshua did it?

Answer 18

Well, if there is just one false statement, so that makes the whole thing false, right?

Answer 19

So, I can say, that since there is a false statement, the assumption that Joshua didn't break the vase is false.

Answer 20

Look at the 4 statements.

1) Joshua broke the vase.
2) Nathan did not do it.
3) Joshua lied when he said Nathan did not do it.
4) Joshua did it.

Think about how you could have 1 false statement.

Answer 21

Then aren't they all contradicting each other????

Answer 22

Are they? Some of them agree with each other, don't they?

Answer 23

Darling, think of it this way.
Assume statement 1 is false. Now go through the other statements and see if that makes sense.

Answer 24

Darling, I'm sorry your thread got derailed. Back to what you were saying =)

Answer 25

@itscheli13, can you try to post your question, to get help for it? Really, I don't want an argument here started over nothing but bad manners. And @SmoothMath , let me just think it out for a second....

Answer 26

And doesn't that mean that the fourth statement is false, also?

Answer 27

Darling, that's correct. If 1 is false, then 4 has to be false also.

Answer 28

Ok, so do I always have to assume the first one is false?

Answer 29

Darling, there's not some formula or method I can give you for figuring these out. You just need to work on thinking through them logically.

Answer 30

hmmm... ok. Oh... So if there is at least one false statement, then you proven your conclusion true, correct?

Answer 31

I think I am starting to get it now....

Answer 32

So first I would assume the opposite of the conclusion, and if there is a false statement, I've proven my conclusion true! Ok!

Answer 33

:)

Answer 34

Thanks!!!!!!