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riddles >> hard >> Re: Logical Nonsense
(Message started by: prince on Apr 10th, 2003, 11:40am)

Title: Re: Logical Nonsense
Post by prince on Apr 10th, 2003, 11:40am

on 04/10/03 at 10:52:10, THUDandBLUNDER wrote:
Therefore, no wise young pigs...

Not true.  A wise young pig [hide] can eat penny-buns, just not dance on tight ropes, be a balloonist, or carry an umbrella [/hide] and I think, still lunch in public.  I am assuming that not all pigs are fat.

Title: Re: Logical Nonsense
Post by Ulkesh on Apr 10th, 2003, 11:44am
The only way the sentences are logically consistent, is if no young, wise pigs... [hide]are balloonists[/hide] (I think).

Title: Re: Logical Nonsense
Post by aero_guy on Apr 10th, 2003, 12:28pm
Ulkesh, that isn't true.  I have found a perfectly consistent answer saying that they are [hide]baloonists[/hide].  I am having a little trouble fitting the may and shouldn't statements into a logical construct, but I seem to get as an answer:

[hide]no wise young pigs eat penny-buns[/hide]

Title: Re: Logical Nonsense
Post by Ulkesh on Apr 10th, 2003, 2:10pm
Ok, I'll go through the logic of my answer...

[hide]
Numbering the statements 1-9.

If a wise young pig is a balloonist...
From statement 3: He takes an umbrella.
8: He therefore looks ridiculous.
5: He is also liable to giddiness
7: He therefore doesn't dance on tightropes
2: He is also treted with respect
1: He doesn't dance on tightropes, and isn't old, so must eat penny buns
9: He is therefore fat

So...

According to statement 4, he ought not to lunch in public.
According to statement 6, he may lunch in public.

Admittedly, neither statement strictly prohibits lunching in public nor requires it, so in a strictly logical sense, young wise pigs can be balloonists as you say. I initally assumed that this was meant as the contradiction in the logic. I'll keep looking for something which agrees with the exact wording of all of the statements.
[/hide]

Title: Re: Logical Nonsense
Post by prince on Apr 10th, 2003, 2:20pm
aero_guy, I don't think young wise pigs can be balloonists, and I'm pretty sure they can [hide] eat penny-buns [/hide].  Can you explain the situation wher they can be balloonists?

Title: Re: Logical Nonsense
Post by Ulkesh on Apr 10th, 2003, 2:28pm
Now I think about it aero_guy, your answer leads to mine...

[hide]

From statement 1, a youngster who doesn't eat penny-buns must dance on tightropes. From 7, he therefore isn't liable to giddiness. From 5, he therefore doesn't go up in balloons!

[/hide]

Title: Re: Logical Nonsense
Post by aero_guy on Apr 11th, 2003, 9:24am
Acutally, my error was in your second to last step with the penny buns.  I agree on the answer.

Title: Re: Logical Nonsense
Post by THUDandBLUNDER on Apr 11th, 2003, 12:52pm

Quote:
I agree on the answer.

So what's the answer? Please write it on one line using logical connectives.

No wise young pigs...?

Title: Re: Logical Nonsense
Post by Ulkesh on Apr 11th, 2003, 6:51pm
My answer is thus...

[hide]
So...

According to statement 4, he ought not to lunch in public.
According to statement 6, he may lunch in public.

Therefore no wise young pigs can be balloonists, as these statements contradict themselves...!
[/hide]

This is the best contradiction I can find... see my reasoning above for the thought process. If there is anything better, I'm interested to hear it...

Title: Re: Logical Nonsense
Post by THUDandBLUNDER on Apr 12th, 2003, 4:15am

Quote:
This is the best contradiction I can find... see my reasoning above for the thought process. If there is anything better, I'm interested to hear it...

I don't think looking for contradictions is the best way to solve this. Rather, one should try to find something which is implied by 'wise young pigs', and then take its negation. To make things simpler, we can write out the statements in shorthand. Let:

D = Dances on tight-ropes
E = Eats penny-buns
Y = Young (equals 'not old')
P = Pig
G = liable to Giddiness
Re = treated with Respect
W = Wise
B = goes up in Balloons
U = takes an Umbrella
R = looks Ridiculous
L = may Lunch in public
F = Fat

We can now rewrite the statements as:

1] not(D) and not(E) => not(Y)
2] P and G => Re
3] W and B => U
4] R and E => not(L)
5] Y and B => G
6] F and R and not(D) => L
7] W and G => not(D)
8] P and U => R
9] not(D) and Re => F

We now need to find something which implies not(W and Y and P).



Title: Re: Logical Nonsense
Post by cho on Apr 12th, 2003, 5:18am
There are two ways to interpret crucial clue number 6. "Fat creatures who look ridiculous may lunch in public if they do not dance on tight-ropes." One: They may eat in public (but they don't have to) provided they meet all the other usual requirements for public eating (no shoes, no shirt, no service would naturally override rule 6, for example).
In that case No wise young pigs who balloon ought to eat in public.
Or (the more likely intent) Two: They may eat in public because the rule makers have ascertained that all who are described in this rule meet all other requirements, and no contradictions ever occur.
In that case No wise young pigs are balloonists.

Title: Re: Logical Nonsense
Post by THUDandBLUNDER on Apr 12th, 2003, 5:28am
cho, you don't need to take the title of this thread so literally. ;)

All the information you need is in my previous post.

Title: Re: Logical Nonsense
Post by cho on Apr 12th, 2003, 6:45am
Oh, sure, and when some restaurant loses its license because it served penny buns to a ridiculous tightrope walker, or they get sued for refusing to serve him, are you going to pay for their lawyer? I don't think so. What do you do when a hippo who's not wearing a shirt insists that rule 6 says he can eat in public? I'm a strict construction constitutionalist, and I think it matters what the rules say. Just to prove it, I'm going to go to lunch today wearing no pants, cuz the rules only say "No shoes, no shirt, no service."

Title: Re: Logical Nonsense
Post by THUDandBLUNDER on Apr 12th, 2003, 7:08am
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Title: Re: Logical Nonsense
Post by Chronos on Apr 13th, 2003, 1:14pm

Quote:
One: They may eat in public (but they don't have to) provided they meet all the other usual requirements for public eating (no shoes, no shirt, no service would naturally override rule 6, for example).
If you take this interpretation, then that statement is completely empty.  From it, we can make absolutely no inferrences at all about who can or cannot eat in public.  Note that that statement, by itself, at least, does not imply that "Fat creatures who look ridiculous and who do dance on tightropes may not eat in public".

Title: Re: Logical Nonsense
Post by THUDandBLUNDER on Apr 13th, 2003, 1:23pm

Quote:

Therefore no wise young pigs can be balloonists, as these statements contradict themselves...!

This is the best contradiction I can find... see my reasoning above for the thought process. If there is anything better, I'm interested to hear it...

Ulkesh, you have cleverly proved that no wise young pigs are balloonists.

Does this mean that all non-balloonists are wise young pigs? If not, then your answer is incomplete.

Title: Re: Logical Nonsense
Post by Ulkesh on Apr 14th, 2003, 4:49am
I'm not quite sure what you're getting at Thud.

I've shown that wise young pigs can't be balloonists. This is what you asked for initally. Of course, this doesn't mean that all non-balloonists are wise young pigs, but the proof of that isn't asked for.

I've also done a quick google search, and although I can't find a full solution to the question with workings, I've found that my answer is correct, so presumably my workings are.

Title: Re: Logical Nonsense
Post by Ulkesh on Apr 14th, 2003, 8:47am
Hey Thud, you just deleted what I was about to reply to! ;)

Anyway, I've had a think and I see what you mean. Wise young pigs can't be balloonists, but that doesn't mean there isn't anything else that can be logically deduced and applied to them.

However, the original riddle (which I found on google), simply states 'show that no wise young pigs are balloonists'. I think this puzzle has been taken and had the 'are balloonists' part removed (I'm not accusing you of doing it, I found a few examples on the web with the same missing text). This changes the riddle completely, and I don't think it's solvable in that form. ie, everything that applies to the set of wise young pigs can't be deduced.

For example, it is impossible to show that being a wise young pig implies solely that you don't go up in balloons (I spent the last 30 minutes trying). This is because there are no statements implying that any particular set necessitates being a balloonist. Being a balloonist can imply other things, but not the other way round. Therefore I think that the only way to solve the original version of the riddle is by showing logical inconsistency if it is assumed that wise young pigs are balloonists. This only shows that wise young pigs are members of one set (which is all the original wording asks for), and I think the riddle can be taken no further than this.

Assuming I'm correct about this, it adds an interesting twist to the riddle itself, and shows how seemingly innocent rewordings can change the riddle entirely.

Title: Re: Logical Nonsense
Post by THUDandBLUNDER on Apr 14th, 2003, 10:43am
Thanks for your long reply, Ulkesh.

Yes, I removed my previous post because I wasn't 100% sure about everything. Never mind, this is a better one. (Jeez...this Chinese beer is stronger than I thought...) I take your point about there being another wording of the problem. However, I spent a lot of time a while back working this out with pen and paper and I am quite sure of my conclusions. (However, Thud has been known to Blunder.) In dealing with this stuff, it is much easier to use the 'shorthand' that I posted previously than to bandy words about. I will post my own solution shortly, but you ought to know about the following identities which are very useful when manipulating many logical propositions:

1) A => B = notB => notA {contrapositive}

de Morgan's laws
2) not(A or B) = notA and notB
3) not(A and B) = notA or notB

We can also, for example, add logical statements:

eg
A => B
and
C => D
implies
A and C => B and D

Also
A and B => C and B
implies
A => C

You ought to manipulate the 'shorthand' version of the puzzle that I posted,
so as to get (W and Y and P) => something

Then not(something) => not(Y and Y and P) {contrapositive}

So, not(something) is the ANSWER!!


Title: Re: Logical Nonsense
Post by Ulkesh on Apr 14th, 2003, 1:05pm
Hehe... we seem to be meeting/sparring a lot on the forums today  ;)

Anyway, I still think it isn't possible (given the puzzle's modification) to get to a point where:

P and Y and W => not(B)

This is because the 2 statements involving balloons both have something implied by going up in balloons, and nothing implying their use. Therefore it isn't logically possible for anything thereafter to imply the use (or lack thereof) of balloons.

Title: Re: Logical Nonsense
Post by Ulkesh on Apr 14th, 2003, 1:59pm
You misunderstand me...

I understand your point clearly: No balloonists are wise young pigs, but that doesn't mean wise young pigs don't belong to another set.

I wasn't proposing that I had proved P and Y and W => not(B) (and no other set), I was proposing that it isn't possible to show that:

P and Y and W => not(B),

given the puzzles's modification using your method, so it's also not possible to get to a point:

P and Y and W => not(B) and some other set

I presume it is possible to get to a point where:

P and Y and W => some other set,

using the method you outlined. However, this answer is also incomplete due to the nature of the modified problem. It wasn't intended as a solution when Lewis Carroll first wrote this, and doesn't make use of all parts of each statement as my original answer does (it can't make use of the balloons for example). As such it isn't such an aesthetically pleasing problem.

What did you obtain as the 'other set', out of interest?

Does anyone else have anything to add to the debate by the way? A fresh perspective can't hurt.

Edit: Ok, it can be shown that wise young pigs don't go up in balloons through the logical inconsistency that arises if they do. It can be shown that young wise pigs are members of other sets using your method, Thud. Things are making a bit of sense now. But since your method doesn't identify all sets that wise young pigs are members of, how do you know using your method will give a complete answer to the modified problem (ie, the version you initally posted)?

Title: Logical Nonsense
Post by THUDandBLUNDER on Apr 14th, 2003, 2:42pm

Quote:
What did you obtain as the 'other set', out of interest?

You go on about Lewis Carroll, about 'modifications', and about this-that-and-the-other. But this puzzle,
as presented here, has not been modified. There is a puzzle and there is a solution - that's all there is to it.

I say that (W and Y and P) => not(B) AND {a non-empty set}

Furthermore, I claim that this is the answer to the puzzle that began this thread. I don't know or care about what Lewis Carroll believed or didn't believe concerning a possibly different puzzle that may or may not have occurred to him two centuries ago while he was pensively scratching his ass after dinner.


Title: Re: Logical Nonsense
Post by Ulkesh on Apr 14th, 2003, 2:57pm
Ok... I'll be absolutely matter-of-fact:

- Being derogatory isn't going to get anyone anywhere.

- You don't deal with my points, right or wrong. I'm explaining my thought processes in my posts. They may well be wrong, but please point out where and how!

- I found the original version of the puzzle on Google. That's it. I've explained what it said, and I know that it is different from what you've posted.

- I see now that a logical deduction can be made using your method. I'll see what I come up with. But I don't see how it could possibly involve balloonists, as I've tried to explain. By the way, I've never seen, let alone used the logical notation you've explained, so don't mind me if I'm not instantly proficient with it.

Edit: Since you've edited your post, Thud, a lot of this post doesn't make sense any more... Anyway, I've tried seeing what I can deduce using your method, and I'm not getting very far with it. I'll leave the puzzle for someone else to finish off. Hopefully any confusion that has arisen will be cleared up.



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