- Is it the case that the left door is the correct one to go through if and only if you are a person A?
Victor has been murdered, and Art, Bob, and Carl are suspects. Art says he did not do it. He says that Bob was the victim's friend but that Carl hated the victim. Bob says he was out of town the day of the murder, and besides he didn't even know the guy. Carl says he is innocent and he saw Art and Bob with the victim just before the murder. Assuming that everyone - except possibly for the murderer - is telling the truth, encode the facts of the case so that you can use the tools of Propositional Logic to convince people that Bob killed Victor.
Is it the case that the left door is the correct one to go through (a?) if and only if you are a person A(b?) ?
BadgerJelly » September 1st, 2017, 11:57 pm wrote:I really don't quite understand this due to the "real life" situation not making sense:
A people always tell the truth and B people always lie.
You want to go through the correct door. There is one person there you can ask which door you should go through, left (L) or right (R). You do not know if the person is an A person or a B person. What question should you ask?
Official Answer:
- Is it the case that the left door is the correct one to go through if and only if you are a person A?
I don't understand why this solves the problem. Let us assume that the correct door is the left one. If you are asking a B person they will say "No," but if you are asking an A person they will "Yes." I guess it works ONLY IF we assume the A and B people understand Propositional Logic and rigidly have to apply themselves to it! haha!
BadgerJelly » September 1st, 2017, 11:57 pm wrote:Basically it is presenting a question that is biconditional so that is why it works?
BadgerJelly » September 1st, 2017, 11:57 pm wrote:The other option posed is to ask how you would answer if you were person A, which would still not help you as far as I can see. If I asked "If you were an A person which door would you take?"
BadgerJelly » September 4th, 2017, 8:37 am wrote:Official Answer:
- Is it the case that the left door is the correct one to go through if and only if you are a person A?
Just reviewed this .. it's BICONDITIONAL! That is why it works.
BadgerJelly » September 5th, 2017, 12:23 am wrote:Check it out yourself. It's on Coursera site "Introduction to Logic", at the end of lesson 2 (Called "Big Game")
BadgerJelly » September 5th, 2017, 12:23 am wrote:PLEASE point out any misunderstanding you see on my part. This has been hurting my head trying to adjust to this new language.
BadgerJelly » September 5th, 2017, 12:23 am wrote:note: It is not a course I am getting certificate for. I am just doing the work because I want to learn more.
BadgerJelly » September 5th, 2017, 4:01 am wrote:Thanks!
I need help/break, it's a pain learning the notion, but I understand it's essential for more complex problems so I gotta persist ...
The proofs are killing me at the moment. The site doesn't really seem to help me understand ... guess I'll just have to press on past some things and see if the next lessons shed light on some of my issues (already hunted on youtube for help, but cannot always find what I need).
Anyway, thanks again. One of the other courses I am doing should help, but internet here is pretty slow so cannot watch the vids right now :(
BadgerJelly » September 5th, 2017, 7:11 pm wrote:They do have discussion forums. I guess the course is either too young for them to have opened up yet, or maybe this course doesn't have them (it is in a different format compared to other courses I am doing. Some of the discussion forums on the other courses I am doing have just opened up so hopefully there will be one for this course soon enough ...)
Thanks again. I have kind of let this one sit for now. Busy trying to figure out Fitch notion ... :S
Luckily I've picked VERY carefully my areas of study so they are all complimenting each other :)
Basically Logic, Mathematics, Neuroscience and Linguistics ... plus work on computing, cryptology and the beginning of economics ... and psychology ... haha! everything is connected!! :D
Seriously the spine of focus is on Math/Logic and Linguistics. I am just so happy I ("have") am a brain to annoy afresh everyday. Set my schedule and have around 40 hours a week to dedicate to studying.
BadgerJelly » September 5th, 2017, 7:11 pm wrote:Seriously the spine of focus is on Math/Logic and Linguistics
mitchellmckain » September 4th, 2017, 7:03 am wrote:How about....
S: Would you say the left door is the correct one?
Now it is self referential, and their nature applies to both the answer to S and to what they would say about the door, so it neatly cancels out the possibility of lying.
If A answers T then we know S is true and since A tells the truth, the left door is the correct one.
If B answers T then we know S is false, and he would not say the left door is the correct one, but since he always lies then we know the left door is the correct one.
If A answers F then we know S is false and since A tells the truth, the left door is not the correct one.
If B answers F then we know S is true, and he would say the left door is the correct one, but since he always lies then we know the left door is not the correct one.
Positor » September 6th, 2017, 10:07 am wrote:mitchellmckain » September 4th, 2017, 7:03 am wrote:How about....
S: Would you say the left door is the correct one?
Now it is self referential, and their nature applies to both the answer to S and to what they would say about the door, so it neatly cancels out the possibility of lying.
If A answers T then we know S is true and since A tells the truth, the left door is the correct one.
If B answers T then we know S is false, and he would not say the left door is the correct one, but since he always lies then we know the left door is the correct one.
If A answers F then we know S is false and since A tells the truth, the left door is not the correct one.
If B answers F then we know S is true, and he would say the left door is the correct one, but since he always lies then we know the left door is not the correct one.
If we clarify S by saying: "Given your nature, would you say the left door is the correct one?", then I think the above solution is sound. Does everyone agree?
B is in effect answering the question "How would you answer if you were a liar?" (because he knows it is his nature to lie), but he answers that question falsely, so his answer is the same as if he were a truth-teller answering the question truly. So T means left is correct, whoever he is; and F means left is incorrect, whoever he is.
someguy1 » September 7th, 2017, 6:16 pm wrote:Example 2) Today is Tuesday iff I am the Pope.
Here we have a statement that is NOT a biconditional. It might be that I'm the Pope and today is Tuesday; and it might be that I'm not the Pope and today is not Tuesday. But it's just as possible that I am the Pope and it's Wednesday, or I am not the Pope and it's Tuesday.
In the case of a biconditional (example 1), the two clauses are "locked together." They must necessarily always have the same truth value.
In the case of a non-biconditional (example 2), the two clauses are not locked together. They may have different truth values.
someguy1 » September 7th, 2017, 6:16 pm wrote:Now let us consider the two clauses:
a) The correct door is the one on the left; and
b) The speaker being questioned is a liar.
Is this a case of example 1 or example 2? Clearly it's 2. These clauses are independent. The correct door might be on the left or right; and the speaker may be a liar or a truthteller.
So now what is the truth value of "The correct door is on the left iff the speaker is a liar?" This is NOT a biconditional because the two clauses are independent of each other. The truth value of "The correct door is on the left iff the speaker is a liar" is FALSE.
It's FALSE no matter what the current truth values of the clauses happen to be. The correct door might be on the left or on the right; and the speaker might be a liar or a truthteller. These two conditions are independent of each other. Either could be true or false without affecting the truth or falsity of the other.
someguy1 » September 7th, 2017, 6:16 pm wrote:The professor is wrong and the problem is cooked. [Do people know that expression? A problem is said to be cooked when its stated solution is wrong].
someguy1 » September 7th, 2017, 6:16 pm wrote:Here's the chart, which is not actually a conventional truth table, but just an enumeration of the possibilities.
someguy1 » September 7th, 2017, 6:16 pm wrote:ps2: I googled "two doors liar truth" and got several good links. I am now certain the professor is wrong.
someguy1 » September 8th, 2017, 12:16 am wrote:So when a speaker is asked "Is the correct door on the left iff you are a liar," a truthteller must say NO and a liar must say YES.
mitchellmckain » September 7th, 2017, 8:07 pm wrote:
I have not taught a course in symbolic logic, but I did take a graduate level course in symbolic logic at university and I have taught a variety of classes in math and physics. So I know it is quite typical for a teacher these days to check what is available on the internet and to change the problem so that answering it takes a little more than just copying down what other people say there.
mitchellmckain » September 4th, 2017, 12:03 am wrote:First label the whole question as S. Then label the parts.
S: the left door is the correct one to go through if and only if you are a person A
X: the left door is the correct one to go through
Y: you are a person A
Let the small letters s,x,y be the truth value of these statements.
mitchellmckain » September 4th, 2017, 12:03 am wrote:If A answers T then that tells you S is true which means x=y and since he is an A that means the left door is the correct one.
mitchellmckain » September 4th, 2017, 12:03 am wrote:If B answers T then that tells you S is false which means x<>y and since his is not an A that means the left door is the correct one.
mitchellmckain » September 4th, 2017, 12:03 am wrote:If A answers F then that tells you S is false which means x<>y and since he is an A that means the left door is not the correct one.
mitchellmckain » September 4th, 2017, 12:03 am wrote:If B answers F then that tells you S is true which means x=y and since he is not an A that means the left door is not the correct one.
someguy1 » September 7th, 2017, 9:47 pm wrote:If I am missing something, please tell me exactly what it is I'm missing. Tell me why I'm wrong. I would not be surprised if I am. But I have been at this for several days now and simply can't see how the statement in question is a biconditional.
mitchellmckain » September 1st, 2017, 4:46 am wrote:This is right there in the truth table above.
As BJ explained, this is termed "vacuously true."
This is a feature of symbolic logic and people have a hard time with it because the English meaning of the word is often different. For example...
If the moon is made of green cheese then the air is the lightest element.
If A then B.
In English we think of this as wrong because the first does not give or imply the second. But in symbolic logic, the implication kind of incorporates the idea that a false premise can lead to anything being accepted as true. The implication in symbolic logic is ONLY saying that in the case that A is true then we know that B is true. Thus the only counter example is when A is true but B is not true.
someguy1 » September 7th, 2017, 9:47 pm wrote:Every point you made in this post was an ad hominem.
mitchellmckain » September 8th, 2017, 12:19 am wrote:Another suggestion I have for you is to look up "symbolic logic."
The truthteller's answers all have the truth-value T, so if left is correct, he would answer (in reply to the question "Is left correct?"): "Yes, left is correct". So, for the truthteller, the truthful answer to Q is Yes; and he truthfully answers it "Yes".
The liar's answers all have the truth-value F, so if left is correct, he would answer (in reply to the question "Is left correct?"): "No, left is not correct". So, for the liar, the truthful answer to Q is No; but (being a liar) he falsely answers it "Yes".
If right is correct, then for the truthteller the truthful answer to Q is No; and he truthfully answers it "No".
If right is correct, then for the liar the truthful answer to Q is Yes (he would say left is correct in order to lie consistently); but he falsely answers Q "No".
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