But Exactly Which One?
If these statements are all logical, then exactly how many of them is(are) true?
(1) Exactly one of the other two statements is true. (2) Exactly one of the other two statements is true. (3) Exactly one of the other two statements is true.
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3 solutions
Yep, pretty much
TL;DR: ( 1 , 2 , 3 ) = ( T , T , F ) , ( T , F , T ) , ( F , T , T ) , ( F , F , F )
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Yes , and just to add , a little bit more synthetic approach would be to consider firstly the number of true and false statements and guide the solution on that. One of the most interesting thing I find about this kind of problems is the understanding of their system of referential statements to which actually in abstract thinking it can be said that makes them possible or in other words the study of their innate coherence and would you like to say please what does TL and DR mean ?
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Glad you enjoyed this question. Would you like to post some variation of this type of questions?
TL;DR is an internet slang, which stands for "Too long; didn't read". In other words, I've written up a synopsis for your answer.
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@Pi Han Goh – Then it can almost be said that my answer would be more like a TL , DR stuff not to speak about the fact that it is a little bit unclear but that because it is more of a sketched answer and thanks. Hmmm , I think I know an interesting problem with true and false statements which refer to themselves so I'll post that one then.
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@A A – Looking forward to it!
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@Pi Han Goh – Yea I posted it. I don't know if it appears but it's named "true and false statements".
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@A A – Got it ! Reshared to increase publicity.
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@Pi Han Goh – I was going to say that mathematics is not about marketing and publicity (and I have no doubt you agree) but that's a nice thing to do from you so thanks and I hope you will like it.
I also like a lot a problem you posted on logic a while ago with fractions and just wanted to say that for some time to you because it's almost fascinating so thanks again.
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@A A – Glad you liked my questions! Here's the collection of problems that I've made .
Do post more problems!
FYI: I tried solving your question earlier but I submitted 2 wrong answers without realizing that they're wrong beforehand. Will be making sure I got my facts right before making my final attempt!
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@Pi Han Goh – Does FYI means for your information and , well , maybe I will post some more if you advise me and yes I surely like your questions , go on posting brilliant questions too please ! Good luck with the problem , but know that the answer starts with 0 and you can write it like that even if it is not taken into account when it is introduced.
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@Pi Han Goh – NP (that stand for no problem and not something else). Now I'll let you concentrate.
@Pi Han Goh – I tried too to solve one of your problems but there seems to be two solutions or at least a little bit unclear so maybe you can help me clarify it one day.
It's called Large Tic Tac Toe Tactics Number 2 and I'll post the reasons of why I think there are two solutions there though not today if u want to discuss it.
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@A A – Feel free to report the question.
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@Pi Han Goh – Ok then but not now. If u are still confused about that problem I posted you may take a break.
Not enough info to find because if I had this card everyone is lying.So in conclusion there is not enough information.Denfinately not TMI
Basic solution, if all statements are logical with the same statements. Then it will be void. All are logical but they share one statement. Exactly one of the other two is true. Then we put it in an equation, where: (2-1)^3x = 1, Leaving x = infinity which is void
Taking the statements just in an abstract way of thinking or in another way of saying it just in their form in thinking (which can also be characterized as "a priori" in the large use of the term I think) it can be said that all the statements say something about the other 2 statements and considering further this form in thinking for assigning a truth value for one statement there will be given some "fixed" truth values to the other statements to which it refers which can be proved to be or not consistent (that is , it can be showed that there is no contradiction in what assigning a truth value for one statement would imply therefore making it a possible case scenario for the entire number of statements and more generally by their interrelations in the system of references of the statements) for the fixed truth values of the other statements which in turn refers to the truth value of the statement taken into account and since taking one statement it refers to all the other statements of the system it can be said that it determines the truth values of the entire system or at least that this is the case in this situation therefore being sufficient to verify just by assigning truth values to only one statement.
Doing that observe that if there is a statement which is true then the other 2 will have to be one true and the other false which is a consistent case for the entire system therefore being possible to be 2 true propositions and 1 false and that if one of the statements would be false then that would mean that either the others are both true or both false which leads either to the case where one statement is true which was considered consistent or to the case where if both are false which is also possible to the case where none of the statements is true , therefore being 2 possible outcomes and no way to the determine which one is.