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Which answer in this list is the correct answer to this question? (2017)

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Re: Which answer in this list is the correct answer to this question? (2017)

#91

Post by hokkos »

colanderman wrote: post #88
hokkos wrote: post #74

With Z3 : https://rise4fun.com/z3 (declare-const a Bool) (declare-const b Bool) (declare-const c Bool) (declare-const d Bool) (declare-const e Bool) (declare-const f Bool) (define-fun conjecture () Bool (and (= a (and b c d e f)) (= b (and (not b) (not c) (not d) (not e) (not f))) (= c (and a b)) (= d (or a b c)) (= e (and (not a) (not b) (not c) (not d))) (= f (and (not a) (not b) (not c) (not d) (not e))) (xor a b…

Implication is not strong enough. That permits e.g. f to be true and e to be false. Also I don't know the specifics of the language that tool uses, but typically variadic XOR simply constrains that an odd number of its operands are true. (It so happens that there are no solutions to this problem with 3 or 5 true answers.)

I changed the solver as it would crash when I corrected my code, and redone it with z3 online.

Re: Which answer in this list is the correct answer to this question? (2017)

#92

Post by northern-lights »

cyborgx7 wrote: post #29
AstralStorm wrote: post #25

Earlier quoted context omitted.

Your answer above is incorrect in a very funny way. "At random" implies an uninformed prior, but the question presupposes there's a correct answer, as 0% is missing. 0% and 100% are indefensible for any uninformed prior. There are two answers giving the correct probability for uniform prior. One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of…

>0% and 100% are indefensible for any uninformed prior. If none of the answers are correct, the chance of picking the correct answer is 0%.

Not quite. Because the chance is 0%, the fact that you were able to pick the choice (with 0%) at all implies a contradiction.

Re: Which answer in this list is the correct answer to this question? (2017)

#94

Post by gpsx »

dtjohnnyb wrote: post #17

Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25%

I think the best language to solve this problem is Excel. It says "circular dependency".

Re: Which answer in this list is the correct answer to this question? (2017)

#95

Post by triska »

cyborgx7 wrote: post #10
jonathanstrange wrote: post #3

It seems that 5 is a winner, as stated in the accepted answer. That's a pity, first I thought the goal of the question was to create an instance of Yablo's Paradox. Yablo's paradox is important because you cannot just argue that the paradox arises from an obviously incorrect definition, as people sometimes do for classical semantic paradoxes.

It would be very boring if it was paradoxical. It would just be a more complicated version of: 1. Statement 2 is wrong. 2. Statement 1 is wrong. Edit: I just looked up Yablo's paradox. It only works because there are infinite statements. Since there is a finite number of statements here, it could not be an instance of Yablo's paradox. Only a circular paradox.

One interesting aspect of this concrete example is that even though the two statements seem contradictory at first sight, there are in fact two assignments of truth values to statements so that no contradiction arises.

For instance, using Scryer Prolog and its SAT solver to model the situation:

    ?- sat(S1 =:= (S2 =:= 0)),
       sat(S2 =:= (S1 =:= 0)).
As answer, we get a symbolic expression that compactly captures all concrete solutions:

    clpb:sat(S1=\=S2)
This means that as long as the truth value of S1 is different from that of S2, the puzzle is solved. This is intuitively admissible, because if one of the statements is false, then the other is true.

It would be different if for example Statement 1 said “Statement 1 is false”, because then there is no satisfiable assignment at all:

    ?- sat(S1 =:= (S1 =:= 0)).
    false.

Re: Which answer in this list is the correct answer to this question? (2017)

#96

Post by davvolun »

I could be wrong, but the question is ill-stated; should be something like 'which of the following statements are true', I think, or maybe 'what is the only true statement in the following list.' It's been awhile since logic classes though, maybe those are essentially the same as the original question, I can't quite figure out what I think is wrong with the original question, it just doesn't seem quite right to me.

Also, 4 is ill-stated -- "One of the above is true" -- does that mean exactly one of the above is true, or at least one of the above is true. Although in that case I don't think it matters because 1/2 are mutually exclusive and 2/3 are mutually exclusive, and the combination of those two means that 1/3 are mutually exclusive., so only exactly one of 1-3 can possibly be true anyway.

Re: Which answer in this list is the correct answer to this question? (2017)

#97

Post by Enginerrrd »

Asooka wrote: post #68
dtjohnnyb wrote: post #17

Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25%

That depends on whether we consider A and D the same answer or not. If we can assume that A does not imply D and vice-versa, then we can pick either A or D and be correct (but not both) - in essence our picking either answer collapses the question's wave-function to be one or the other.

I don't think so. A and B are contradictory. A asserts: (A & !B & !C & !D & !E & !F), B asserts (B & !C & !D & !E & !F) which would imply B and !B therefore A is false. Only E (or 5 depending on notation) can be true without contradiction.

Re: Which answer in this list is the correct answer to this question? (2017)

#99

Post by tyre »

jonathanstrange wrote: post #3

It seems that 5 is a winner, as stated in the accepted answer. That's a pity, first I thought the goal of the question was to create an instance of Yablo's Paradox. Yablo's paradox is important because you cannot just argue that the paradox arises from an obviously incorrect definition, as people sometimes do for classical semantic paradoxes.

In my opinion there isn't an answer to the question.

The italicized _this_ is what's important. You need to answer the question itself. As far as I can tell, everyone is caught up reading the answers as

1. All of the below _are true_. 2. None of the below _are true_.

etc.

but the answers don't say that. They don't refer to other answers. The are direct responses to the question. None of those answers make sense in context.

"Which answer in this list is the correct answer to this question? All of the above." That doesn't make sense.

"All of the above _are true_" (etc.) would make sense, but as stated none of the answers provided offer a coherent response to the question.

Re: Which answer in this list is the correct answer to this question? (2017)

#100

Post by lovasoa »

This is the kind of things that are a real pleasure to model in Haskell. Here is a nice solution:

    solve funcs = filter (matches funcs) (possibilities funcs)
    matches funcs truths = truths == zipWith (($).($truths).flip) funcs [0..]

    possibilities [] = [[]]
    possibilities (x:xs) = concatMap (\x -> [True:x, False:x]) (possibilities xs)

    all_of = ((and.).)
    one_of = ((or.).) 
    none_of = (((not.or).).)

    the_above = take
    the_below = drop.(+1)

    main = mapM_ putStrLn $
      zipWith
        (\i s -> "Answer number " ++ (show i) ++ " is " ++ (show s))
        [1..] $
        head $ solve [
          all_of  the_below,
          none_of the_below,
          all_of  the_above,
          one_of  the_above,
          none_of the_above,
          none_of the_above
        ]
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