[Guest]

Hi

<Example>

given these two statements:

"All men drink beer."

"I am a man."

you could logically deduce that I drink beer.

<end of example>

Ok, now for the slightly harder one. Given these two statements:

"All politicians are thieves."

"No composer is a politician."

What, if anything, can you logically deduce from these two statements?

"No politicians are composers"

[Guest]

What, if anything, can you logically deduce from these two statements?

I like beer.

[HoustonHokie]

you'd like to say that no composers are theives, but that's not valid with the information we've got. Politicians are a subset of the overall group of theives, and, even though there is no overlap between composers and politicians, it is entirely possible that composers are a subset of theives as well, either in whole or in part. Or, they might not be theives at all. I guess the most we can say is that some theives are politicians.

[Guest]

"All politicians are thieves."

"No composer is a politician."

What, if anything, can you logically deduce from these two statements?

"No politicians are composers"

Nothing.

And no, you can't say that no composers are thieves. I like to use chocolate as an example.

All Hershey's is Chocolate.

No Nestle is Hershey's.

So, no Nestle's is Chocolate.

But that's not true. So substitute 'Hersheys' for 'Politicians', 'Chocolate' for 'Theives', and 'Nestle' for 'Composers'. And you see why it doesn't work.

If I've missed anything (this is the only one i think people might assume to be deducable), let me know.

[Shakeepuddn]

"All politicians are thieves."

"No composer is a politician."

Conclusion: No one knows where hapa haole came from.

[Guest]

The official answer is...

There are thieves who are not composers

[Guest]

you'd like to say that no composers are theives, but that's not valid with the information we've got. Politicians are a subset of the overall group of theives, and, even though there is no overlap between composers and politicians, it is entirely possible that composers are a subset of theives as well, either in whole or in part. Or, they might not be theives at all. I guess the most we can say is that some theives are politicians.

That's some fine reasoning there.

[Guest]

You can't conclude anything! Not enough information.

[Guest]

You can't conclude anything! Not enough information.

mmmm check out the answer in post #6 :0)

[bonanova]

The official answer is...

There are thieves who are not composers

I agree: there is not enough information to deduce the official answer.

The existence of at least one politician.

What we are given is All P are T. and No C is P.

It does not follow from these that There are T who are not C.

Add the statement: Some P exist, or permit use of

the common knowledge that politicians exist, and we're ok:

An instance of a P gives an instance of a T which is not a C.

Consider:

1. All Unicorns are Mythical Creatures.
   
2. No Composers are Unicorns.
   

It does not follow that there are Mythical Creatures who are not composers.

[Guest]

I agree: there is not enough information to deduce the official answer.

The existence of at least one politician.

What we are given is All P are T. and No C is P.

It does not follow from these that There are T who are not C.

Add the statement: Some P exist, or permit use of

the common knowledge that politicians exist, and we're ok:

An instance of a P gives an instance of a T which is not a C.

Consider:

1. All Unicorns are Mythical Creatures.
   
2. No Composers are Unicorns.
   

It does not follow that there are Mythical Creatures who are not composers.

Sorry, is it not common knowledge that politicians (and indeed composers and thieves) exist? Does it really need spelling out?

In the same way, in my first example, would I need to explain that men and beer and I exist?

The fact that they exist in the question makes it reasonable to assume that we are talking about a body of existing politicians...

In the same way, in your example, the very fact that you mention Unicorns means that they exist, for the purpose of the question...in fact, I'd pretty much guarantee that anyone reading the word will be imagining what one looks like...

Seems to me that it stumped you, so you look for a technicality ;0)

maybe the official answer should read "Some thieves are not composers" or maybe rephrase the question to "All the politicians..."

[bonanova]

Agree that it's common knowledge that at least one politician exists.

But the puzzle asks

What, if anything, can you logically deduce from these two statements?

In modern logic, the statement All P are T does not assert the existence of a P.

That's why All Unicorns are Mythical Creatures makes sense, even tho there are no Unicorns [that we know of].

Or a posted sign saying All Trespassers will be Prosecuted does not imply that someone is trespassing.

Also, in the example about beer, since it's common knowledge [to me anyway] that I am a man, I would not have needed that statement. Since you supplied it, I adopted a consistent approach to the puzzle question.

Net:

I was being picky.

[Guest]

Net:

I was being picky.

Agreed, but you're so good at it! I'll try and make my next puzzle wording less ambiguous (although looking through the posts here, I think it's impossible!)

[Guest]

no offense to anyone on this website, but boy are we geeks, picking on every single detail, looking for every single loophole!