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a puzzle for your thoughts

S

SWScorch

Diamond Member
Here's a good logic riddle for ya. I think I got it, but let's see how ATOT fares.

Assume there is an infinite set of politicians in the USA. Given any set of n politicians, if one of them is a liar, all of them are liars. This is true if n = 1. If we assume it is true for any value k, then we assume, for instance, that the first one is a liar, and thus all k of them are liars. Wecan use this statement as being true to deduce that the statement is true for k + 1, since if the first one is a liar, as per assumed for k, then all k + 1 are liars.

There is a flaw in this logic; do you know what it is?

Anyway, yes, this is for a class, but it's for extra credit, and I've already worked on it and think I have the answer and want to see if I'm right. So dont flame me for asking for help on here. 😛
 
I don't see how it follows that if it's true for a group of k politicians that it's true for a group of k+1.
 
Originally posted by: TuxDave
I don't see how it follows that if it's true for a group of k politicians that it's true for a group of k+1.
Click to expand...

If you have a group of 5 politicians in a line and the first one is a liar, the logic in this says they are all then liars. Then if another politician comes and joins the group (k+1) and the 1st liar is still there then according to this logic the new politician is also a liar since he is part of the group.
 
Induction people, INDUCTION! Google it. But I'm guessing that somehow you can't get that k+1 = k+1
 
Originally posted by: Mo0o
Originally posted by: TuxDave
I don't see how it follows that if it's true for a group of k politicians that it's true for a group of k+1.
Click to expand...

If you have a group of 5 politicians in a line and the first one is a liar, the logic in this says they are all then liars. Then if another politician comes and joins the group (k+1) and the 1st liar is still there then according to this logic the new politician is also a liar since he is part of the group.
Click to expand...

But if you're using induction and saying that it's true for a set of k politicians, when you're given k+1 of them, can you only conclude that at least K are liars?
 
Your interpretation is wrong.

You show it's true for the first politician. You then assume it's true for the kth politician, and then you use that fact to prove that it's true for the k+1th politician. If you can do this, then you have proved that they are all liars.

The fact is that while you can find one liar, you won't be able to say for sure that the next one is a liar based on the previous one being a liar.

It's like saying: I flip a coin, it comes up tails. I then flip it again, say it comes up tails, then the next one will be tails too, and therefore whenever I flip a coin it will always be tails. Not quite right.

But in reality, everyone lies... so all politicians lie.
 
<My crazy guess> Assuming k elements is a subset of n, there is no guarantee that the k+1 subset contains the same elements found in k subset. This means it's possible that the lying lawyer found in subset k wouldn't be found in subset k+1. Thus, you can't prove by induction that the case is true for k+1</My crazy guess> 😀
 
Originally posted by: SWScorch
Here's a good logic riddle for ya. I think I got it, but let's see how ATOT fares.

Assume there is an infinite set of politicians in the USA. Given any set of n politicians, if one of them is a liar, all of them are liars. This is true if n = 1. If we assume it is true for any value k, then we assume, for instance, that the first one is a liar, and thus all k of them are liars. Wecan use this statement as being true to deduce that the statement is true for k + 1, since if the first one is a liar, as per assumed for k, then all k + 1 are liars.

There is a flaw in this logic; do you know what it is?

Anyway, yes, this is for a class, but it's for extra credit, and I've already worked on it and think I have the answer and want to see if I'm right. So dont flame me for asking for help on here. 😛
Click to expand...

uh...you're already given that in a set of n politicians, if one is a liar, then all of them are liars. Why are you trying to prove it?

What are you really trying to prove?
 
Originally posted by: chuckywang
uh...you're already given that in a set of n politicians, if one is a liar, then all of them are liars. Why are you trying to prove it?

What are you really trying to prove?
Click to expand...

I think it's not 'given' but you're supposed to prove it. It's obviously true for the first politician; if they're a liar, then all one of them are liars. But you can't do anything with that result. So there's no rule by which to assume the Kth politician, and therefore no way to prove the K+1th politician.
 
Originally posted by: chuckywang
Originally posted by: SWScorch
Here's a good logic riddle for ya. I think I got it, but let's see how ATOT fares.

Assume there is an infinite set of politicians in the USA. Given any set of n politicians, if one of them is a liar, all of them are liars. This is true if n = 1. If we assume it is true for any value k, then we assume, for instance, that the first one is a liar, and thus all k of them are liars. Wecan use this statement as being true to deduce that the statement is true for k + 1, since if the first one is a liar, as per assumed for k, then all k + 1 are liars.

There is a flaw in this logic; do you know what it is?

Anyway, yes, this is for a class, but it's for extra credit, and I've already worked on it and think I have the answer and want to see if I'm right. So dont flame me for asking for help on here. 😛
Click to expand...

uh...you're already given that in a set of n politicians, if one is a liar, then all of them are liars. Why are you trying to prove it?

What are you really trying to prove?
Click to expand...


Yeah seems like a circular argument to me. You are assuming your conclusion then proving it by using the assumption itself.
 
Originally posted by: 3chordcharlie
Originally posted by: chuckywang
uh...you're already given that in a set of n politicians, if one is a liar, then all of them are liars. Why are you trying to prove it?

What are you really trying to prove?
Click to expand...

I think it's not 'given' but you're supposed to prove it. It's obviously true for the first politician; if they're a liar, then all one of them are liars. But you can't do anything with that result. So there's no rule by which to assume the Kth politician, and therefore no way to prove the K+1th politician.
Click to expand...


Ah.. If k = liars and you need only one to be all liars, k + 1 = liars?


excuse my lack of logic.
 
You're assuming if one is a liar in a set of k, all are liars. That says nothing about a k+1 set. If all are liars in a set of k, then adding one element will make that assumption irrelevant. There is no way to link a set of k to a set of k+1.
 
Originally posted by: chuckywang
You're assuming if one is a liar in a set of k, all are liars. That says nothing about a k+1 set. If all are liars in a set of k, then adding one element will make that assumption irrelevant. There is no way to link a set of k to a set of k+1.
Click to expand...



Edit: well that was fun for me 🙂
 
Originally posted by: DaveSimmons
Are you paraphrasing, or did the professor word it with that exact vagueness?
Click to expand...

I paraphrased a little, but the question really is that vague. By the way,no one has answered with my theory yet... Which probably means that I'm wrong.
 
Originally posted by: SWScorch
Originally posted by: DaveSimmons
Are you paraphrasing, or did the professor word it with that exact vagueness?
Click to expand...

I paraphrased a little, but the question really is that vague. By the way,no one has answered with my theory yet... Which probably means that I'm wrong.
Click to expand...

What is your theory then?
 
My theory is that while the statement holds true for n = 1, there is no reason why it holds true for n > 1. Actually, now that I mention it, silverpig pretty much said what I was thinking, but in a different way.
 
wait..


If all politicans are liars, n=1
If none of the politicans are liars, n=0


so n is an integer with possible values of 0 and 1. This says that the number of politicians, n, is either set to 0 or 1.

n therefore represents all of the politicians as well as their liability. The problem has stated that one variable serves two purposes.

The whole k thing is irreverent to put it lightly. K is said to represent the number of politicians although n has already been set to that 😕 k + 1 says that I have just added a politican, and a liar at that. to the total number of politicians 😕


A variable is either dependant or independat IIRC; it is not both.




 
Originally posted by: Goosemaster
wait..


If all politicans are liars, n=1
If none of the politicans are liars, n=0


so n is an integer with possible values of 0 and 1. This says that the number of politicians, n, is either set to 0 or 1.

n therefore represents all of the politicians as well as their liability. The problem has stated that one variable serves two purposes.

The whole k thing is irreverent to put it lightly. K is said to represent the number of politicians although n has already been set to that 😕 k + 1 says that I have just added a politican, and a liar at that. to the total number of politicians 😕


A variable is either dependant or independat IIRC; it is not both.
Click to expand...

You are way off here... where did you get n=0 and n=1?
Also, ir·rev·er·ent adj. 1. Lacking or exhibiting a lack of reverence; disrespectful.
 
Originally posted by: ArmenK
Originally posted by: Goosemaster
wait..


If all politicans are liars, n=1
If none of the politicans are liars, n=0


so n is an integer with possible values of 0 and 1. This says that the number of politicians, n, is either set to 0 or 1.

n therefore represents all of the politicians as well as their liability. The problem has stated that one variable serves two purposes.

The whole k thing is irreverent to put it lightly. K is said to represent the number of politicians although n has already been set to that 😕 k + 1 says that I have just added a politican, and a liar at that. to the total number of politicians 😕


A variable is either dependant or independat IIRC; it is not both.
Click to expand...

You are way off here... where did you get n=0 and n=1?
Also, ir·rev·er·ent adj. 1. Lacking or exhibiting a lack of reverence; disrespectful.
Click to expand...

It's two in the mornign dammnit😛

And my logic sucks....I can do math in general (Iam in diff eq and finished calc 1-3) but I jsut failed physics 1 again🙁

I was thinking of taking philosophy to help me out with it.

As for irreverent, I am quite generous when it comes to using lavish adjectives 😀
 
Originally posted by: Goosemaster

It's two in the mornign dammnit😛

And my logic sucks....I can do math in general (Iam in diff eq and finished calc 1-3) but I jsut failed physics 1 again🙁

I was thinking of taking philosophy to help me out with it.

As for irreverent, I am quite generous when it comes to using lavish adjectives 😀
Click to expand...

My prof. in probability did a bunch of logic exercises with us. It is pretty interesting and I would take a phil class if I had the time.
 
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