I just started reading Oscar Levin's Discrete Mathematics online textbook, and this was exactly what I needed to better grasp these intro topics. Really awesome explanation. Liked and subbed!
Glad it’s helpful! It’s from a class I taught using Levin’s book. Check the whole playlist as you read on. And good luck with it - it’s a great subject to learn!
For the last challenge: With these rules, it’s impossible for any islander to say “I am a knave”. If he is lying, then he would be a knave, and his statement would be true, a contradiction. So he is not lying, is a knight, and the trueness comes from the second part of his “or” statement. They are both knights.
@@hontema The final challenge? I think it is "(not P) OR Q" where P is Person A is a Knight and Q is Person B is a Knight. Then you want to look at rows where person A could have said that. There is only one row that works out if you check it out
Raymond Smullian's books are fulled of brainteasers that introduce logic concepts. Knights and knaves are his way of introducing propositional logic but he also has some books introducing combinators (how to mock a mockingbird), the modal logic of provability (forever undecided), and godel theorems (the godelian puzzle book)... I wonder whether people would be interested on videos on those other type of puzzles
@@academyofuselessideas yes! At some point I might make more. These were for a class I taught and so they aren’t like the majority of my channels videos.
Yes. I made this for a course in case students have to miss class in quarantine. I put a poll up to see if there is interest in this or if I should stick with short visual proofs. I’d like to see your take on logic problems!
Thanks! For now I’ll just put it in a playlist because I’m not sure how many more there will be in the series after the first five or so. If I end up doing more perhaps I’ll try a separate channel. :)
There's an old quiz I'd read: "An explorer was captured by a maneater tribe. They will set him free if he can distinguish two people: a "knight" and a "knave" with a single question" The hint is: the knave never admits he's a knave! In this case, you know it's more than that.
This is the general process about how to solve Knights and Knaves problems. You need to describe what each person says logically and then fill in the truth table. You can then check row by row if what each person said agrees with their type. The other way to do this systematically is to use the biconditional connective. I describe this here: th-cam.com/video/Imgus1ispQk/w-d-xo.html
![The Lady or the Tiger Puzzle via Truth Tables [Discrete Math Class]](http://i.ytimg.com/vi/eUYWXqk5Ags/mqdefault.jpg)
![The Lady or the Tiger Puzzle via Truth Tables [Discrete Math Class]](/img/tr.png)
I just started reading Oscar Levin's Discrete Mathematics online textbook, and this was exactly what I needed to better grasp these intro topics. Really awesome explanation. Liked and subbed!
Glad it’s helpful! It’s from a class I taught using Levin’s book. Check the whole playlist as you read on. And good luck with it - it’s a great subject to learn!
For the last challenge:
With these rules, it’s impossible for any islander to say “I am a knave”. If he is lying, then he would be a knave, and his statement would be true, a contradiction. So he is not lying, is a knight, and the trueness comes from the second part of his “or” statement.
They are both knights.
Definitely! Fun to realize that no one can say I’m a Knave. It also pops right out of the truth table if you go that route. :)
@@MathVisualProofs what would the truth table be? i think it'd be p, q, p=¬q, ??? i think i am wrong but idk what would be the answer
@@hontema The final challenge? I think it is "(not P) OR Q" where P is Person A is a Knight and Q is Person B is a Knight. Then you want to look at rows where person A could have said that. There is only one row that works out if you check it out
Raymond Smullian's books are fulled of brainteasers that introduce logic concepts. Knights and knaves are his way of introducing propositional logic but he also has some books introducing combinators (how to mock a mockingbird), the modal logic of provability (forever undecided), and godel theorems (the godelian puzzle book)... I wonder whether people would be interested on videos on those other type of puzzles
Love Smullyan’s books and puzzles for sure!
@@MathVisualProofs I should watch your the lady and the tiger video!
@@academyofuselessideas yes! At some point I might make more. These were for a class I taught and so they aren’t like the majority of my channels videos.
This is quite a bit of change of pace compared to the other videos. I also wanted to eventually cover problems of this kind.
Yes. I made this for a course in case students have to miss class in quarantine. I put a poll up to see if there is interest in this or if I should stick with short visual proofs. I’d like to see your take on logic problems!
@@MathVisualProofs I might cover several Raymond Smullyan books eventually. I practically grew up on his (and Martin Gardner) books.
@@mathflipped yes. All good. I have a short video in this series that might come next about lady/tiger problems.
great intro to prop logic, i hope you decide to put videos of this type together on a separate channel
Thanks! For now I’ll just put it in a playlist because I’m not sure how many more there will be in the series after the first five or so. If I end up doing more perhaps I’ll try a separate channel. :)
9:54 , why did we use 'or' disjunction and why not the and conjunction
There are two situations. One or the other happens. They can’t both happen simultaneously
@@MathVisualProofs Thank you 👍
What should be the statement when a person says that both of them are knave , i think it should be (-p and -q)
@@sheetalgumgol2897 yes. For sure!
Great Work I hope you will continue your pursuit of truth.
Thanks!
There's an old quiz I'd read: "An explorer was captured by a maneater tribe. They will set him free if he can distinguish two people: a "knight" and a "knave" with a single question"
The hint is: the knave never admits he's a knave! In this case, you know it's more than that.
Yes. These puzzles are all great! And most invoke the conditional connective in some way (asking an if then statement of someone).
the comparison for what person A and person B said is basically just using the biconditional to determine when both are true right?
Yes! The follow up video investigates the biconditional in this way.
Here is link : th-cam.com/video/Imgus1ispQk/w-d-xo.html
If for the person that said nothing he would be a knight or a knave, can we use that for B said?
9:55 how do we find in in general can you do a video on that?
This is the general process about how to solve Knights and Knaves problems. You need to describe what each person says logically and then fill in the truth table. You can then check row by row if what each person said agrees with their type. The other way to do this systematically is to use the biconditional connective. I describe this here: th-cam.com/video/Imgus1ispQk/w-d-xo.html
Both are knights and also thank you so much for video. Great Job.
Thanks! Good work on the bonus problem!
very good. The voice is very good too.
Thanks!