Mind Racking Extra Credit Problem

[Titanguy654]

Oh god, my teacher is weird. She gave me some kind of a riddle for extra credit, and I can't solve it! Does anyone want to help me show off for school tomorrow, or just see if they can do it themself? Be my guest:

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In a recent murder case, the police determined, based on the evidence, that whoever the guilty person is, he or she must be color-blind. Mr. Green was arrested for the murder, and he quickly hired an attorney. At the trial, Mr. Green's attorney tried to offer another possible suspect: Mrs. Peacock. In the closing arguements, the prosecution summed up the case and reminded the jury of the key points on which to decide guilt or innocence. The prosecution argued these two arguments:

"If a person is guilty, he or she is color-blind.
Mr. Green Is color-blind.
Therefore, Mr. Green is guilty."

AND
"If a person is guilty, he or she is color-blind.
Mrs. Peacock is not color-blind.
Therefore, Mrs. Peacock is not guilty."

As a member of the jury, what can you conclude based on these two arguements if you know the first two statements of each argument are true? Explain completely.

Also: What is the dead person's name?

 

[A Weary Exile]

I think Mrs. Peacock was the one murdered, that's all I've got.

EDIT: I'm not very good at riddles so no being a dick if this is wrong.

 

[Flap Jack452]

I think I just had an aneurism.

 

[Datalord]

It wasn't Mr. Green, the evidence for his conviction is the inverse of the original statement, which is only true of a biconditional statement (if and only if), you can conclude that Mrs. Peacock is not guilty as well, because the evidence for her innocence is the contrapositive of the original statement, which is true as long as the original statement is.

Mr green may be guilty, but it isn't proven, Mrs Peacock isnt guilty

the dead man is Mr. Buddy, the dead guy in CLUE

The fact that i know that is a little disturbing

 

[Bassman_2]

Something about greenpea? I dunno.

 

[zidine100]

i conclude OBJECTION!.

hmm i would say it was coneral musterd in the dining room with the crowbar,

mr green is guilty,

or every colour blind persion is a criminal.

sorry i have no idea, i just couldnt resist some of these bad jokes.

 

[Titanguy654]

It wasn't Mr. Green, the evidence for his conviction is the inverse of the original statement, which is only true of a biconditional statement (if and only if), you can conclude that Mrs. Peacock is not guilty as well, because the evidence for her innocence is the contrapositive of the original statement, which is true as long as the original statement is.

Mr green may be guilty, but it isn't proven, Mrs Peacock isnt guilty

So what is the name of the dead person? D:

 

[Datalord]

It wasn't Mr. Green, the evidence for his conviction is the inverse of the original statement, which is only true of a biconditional statement (if and only if), you can conclude that Mrs. Peacock is not guilty as well, because the evidence for her innocence is the contrapositive of the original statement, which is true as long as the original statement is.

Mr green may be guilty, but it isn't proven, Mrs Peacock isnt guilty

So what is the name of the dead person? D:

Mr Buddy, i edited my original post

Thats the guy who died in the original game of clue

 

[Samurai Goomba]

Both statements are logical fallacies and cannot be true. To assume they are true is to acknowledge the validity of obviously fallacious reasoning.

If I were on the jury, I'd avoid weighing in on a verdict until more compelling evidence for or against his guilt was brought forward.

 

[Titanguy654]

Both statements are logical fallacies and cannot be true. To assume they are true is to acknowledge the validity of obviously fallacious reasoning.

Well, thanks for not helping.......

 

[Datalord]

Both statements are logical fallacies and cannot be true. To assume they are true is to acknowledge the validity of obviously fallacious reasoning.

No, the second statement hinges on the contrapositive, so it is true, but the first hinges on the inverse, so it is not necessarily true

 

[ObsessiveSketch]

The dead man in Clue was Mr. "Body." (See what they did there?)

While the heap of logic above (the inverse statement) makes sense, I would work more with the fact that the characters in clue are all named after colors, and are presumed to dress accordingly.

Perhaps the colorblind killer killed the wrong person, because he couldn't tell what color they were?

The inverse statement is rarely used because it's just such a ridiculous way of thinking "We know the killer is gay...the suspect is gay, so he must be the killer!" By this logic, every gay person could be/"is" the killer.

hope that helps. I'll keep thinking

 

[Trivun]

It wasn't Mr. Green, the evidence for his conviction is the inverse of the original statement, which is only true of a biconditional statement (if and only if), you can conclude that Mrs. Peacock is not guilty as well, because the evidence for her innocence is the contrapositive of the original statement, which is true as long as the original statement is.

Mr green may be guilty, but it isn't proven, Mrs Peacock isnt guilty

So what is the name of the dead person? D:

Mr Buddy, i edited my original post

Thats the guy who died in the original game of clue

In the UK, it's Dr Black.

Right, so I do Mathematical Logic as a module on my maths course, so I was actually typing a detailed look using propositional logic (complete with symbols and rules and everything) as I've been taught. Then like an idiot I refreshed the page by accident and lost it all. However, the crux of the argument can be summed up quite easily without the need for such detail, which is only really necessary for the theory behind logic and for more advanced and complicated logic problems. Anyway, Mr Green is colour-blind but that doesn't mean that he's the killer. There is no way Mrs Peacock can be the killer as she isn't colour-blind and the statement is already taken as true that the killer is colour-blind. So we have two situations. One is that Mr Green is the killer, the other is that neither person is the killer. The result is therefore in flux until further evidence (i.e. true statements) are produced.

 

[Titanguy654]

It wasn't Mr. Green, the evidence for his conviction is the inverse of the original statement, which is only true of a biconditional statement (if and only if), you can conclude that Mrs. Peacock is not guilty as well, because the evidence for her innocence is the contrapositive of the original statement, which is true as long as the original statement is.

Mr green may be guilty, but it isn't proven, Mrs Peacock isnt guilty

So what is the name of the dead person? D:

Mr Buddy, i edited my original post

Thats the guy who died in the original game of clue

In the UK, it's Dr Black.

Right, so I do Mathematical Logic as a module on my maths course, so I was actually typing a detailed look using propositional logic (complete with symbols and rules and everything) as I've been taught. Then like an idiot I refreshed the page by accident and lost it all. However, the crux of the argument can be summed up quite easily without the need for such detail, which is only really necessary for the theory behind logic and for more advanced and complicated logic problems. Anyway, Mr Green is colour-blind but that doesn't mean that he's the killer. There is no way Mrs Peacock can be the killer as she isn't colour-blind and the statement is already taken as true that the killer is colour-blind. So we have two situations. One is that Mr Green is the killer, the other is that neither person is the killer. The result is therefore in flux until further evidence (i.e. true statements) are produced.

Yep, I got that part of it. Now I just need the last part: What is the dead person's name?

 

[rhyno435]

If Mr. Green did it and he accused someone else, being colourblind, he would have to know that the crime could only have been done by someone colourblind, therefore he would have accused someone else who is colourblind.

Since the woman he accused is not colourblind, Mr. Green is not guilty.

I actually have no idea, but that sounded kind of logical.

It probably has something to do with the fact that his last name is Green and he's colourblind.

 

[Samurai Goomba]

Both statements are logical fallacies and cannot be true. To assume they are true is to acknowledge the validity of obviously fallacious reasoning.

No, the second statement hinges on the contrapositive, so it is true, but the first hinges on the inverse, so it is not necessarily true

All guilty people are colorblind, but not all colorblind people are guilty.

Mr. Green might or might not be guilty. Mrs. Peacock can't be guilty, though.

 

[L_Lawliet]

This is a riddle from Clue. Mr. Green and Mrs. Peacock are characters from the classic board game.

My guess is that the person who is dead is Mr. Boddy (two d's). He was the person who died in the classic board game Clue.

As for the guilt/innocense problem, it is certain that Peacock is not guilty as she is not color-blind. The rules of the riddle require the culprit to be color blind, so she is free to go.

Green on the other hand could be innocent or guilty. The fact that he is color-blind keeps him as a suspect, but there are many blind people in the world, and we have no evidence apart from color-blindness to convict Green.

 

[Titanguy654]

Thanks for the help everyone, I'll just name the dead guy as Mr. Boddy then.

 

[Trivun]

Thanks for the help everyone, I'll just name the dead guy as Mr. Boddy then.

That depends, what country are you from? If you're from the UK then it's Dr Black, if you're from anywhere else then it's Mr Boddy.

 

[LilGherkin]

I can conclude you're playing Clue.