Discrete Math - 1.2.2 Solving Logic Puzzles

[@taulguedi637]

This puzzle haunted me for years. With a paper and a little bit of patience I solved it for myself. (Maybe that is childish but... I am so proud!). :)) Thank you for the class. You have a new student.

[@AyhamAlshwaiki]

not childish at all

[@briwitbeck8807]

I am simultaneously taking Discrete Math and Linear Algebra and your courses are helping me immensely. I need online coursework as an ADHD person. In person classes are killing me and you have saved my GPA.

[@sabrinanastasi5809]

The best videos on discrete math on the internet and outside the internet. Thank you!

[@aryamhaske7307]

"Y'all need to grow up and don't invite any of them" I'm dying😂😂 literally most of the time this happens. Awesome Lecture! Thank You for a wonderful exercise with great explanation!

[@Orengelol]

Kimberly you greatly assisted me in Linear Algebra, now you're assisting in Discrete! Thank you for your videos

[@johnathanrhoades7751]

I love the party planning. It’s like “or, of course, you could just not have a party in the first place!” 😂

[@alex-nb3lh]

it would be nice if you elaborated on your reasoning while filling out the truth table in the three friends problem, it is difficult to follow

[@caitlindominguez6071]

I am so thankful I stumbled across your channel. I am in a discrete math class for computer engineering and I am in a different country so I'm learning it in my second language. I am so thankful I have some help in English now.

[@SawFinMath]

So glad I could help!

[@GFh-v1w]

Thank you so much, Miss Brehm for your very helpful tutorials. At first when taking my classes, nothing made sense, but you are breaking it down and making it much easier for me to understand it. Amazing work and I will continue to watch all your videos to comprehend what I am learning.

[@TheAngryMaskSalesman64]

Bob Ross of Discrete Math. Thank you for these videos!

[@SawFinMath]

@@TheAngryMaskSalesman64 Let’s paint some happy equations!

[@randoUser-n4s]

@11:00 Is it possible to answer the propositions in the truth table in terms of T and F, rather than J/notJ, S/notS, K/notK?

[@astrojay5899]

im struggling to understand the Party Planning one.

[@zuko803]

I need 2 days to understand this solving puzzle invitation, now I get it!!! thanks

[@HomeBologn]

I hate when I go to a party and somebody is acting all Kanti.

[@SawFinMath]

That is hilarious!

[@brunilda]

For the knights and knaves puzzle there is a really easy, really cool algebraic method (essentially algebra in the Galois field modulo 2, where the only numbers are 0 and 1, and 1+1=0). We use 0 to represent "false" and 1 for true; then you translate A says "B is a knight" by (A is a knave) + (B is a knight) = 1 (Why? Because is "A is a knave" is true, equal to 1, then "B is a knight" has to be false, equal to 0 to make the equation true; conversely, if "A is a knave" is false, then equal to 0, in order to make the equation true "B is a knight" has to be 1, that is true. Note that p+q=1 is an algebraic translation of p XOR q.) The second statement is (B is a knave) + (A is a knave XOR B is a knave) = 1, that is, (B is a knave) + (A is a knave) + (B is a knave) = 1. Because adding the same thing to itself in GF2 is 0, the second equation resolves to "A is a knave" = 1. From that, plugging in the first equation, "B is a knight" has to be 0, so B is also a knave. Once you understand how this works, a complete solution looks simply like this (with T for knight and F for Knave): 1. A is F + B is T =1 2. B is F + (A is F + B is F) = 1 From 2, A is F = 1; therefore, replacing in 1 + B is T = 1, so B is T = 0.

[@SawFinMath]

Love it! Thanks for sharing!

[@brunilda]

@@SawFinMath And it can be extended to problems with knights, knaves, and normals who tell the truth or lie randomly. Pretty cool algebra in GF(2)

[@ulysses_grant]

This is completely crazy (in a very good way)! I had to rewatch the knights and knaves part about three times to get it. I need so bad to study logic for it to flow naturally, lol. Thank you!

[@chessketeer]

Thank you for a great lesson, Prof. Brehm.

[@mackenzielewis8291]

your videos are extremely helpful! thank you so much for making these

[@SawFinMath]

Glad you like them!

[@DANKAF]

you dont need to fill the table, you can directly eliminate from the possibilities,for example, if you find j -- >s eliminate / if you find s -- > not k eliminate / if you find k -- > not j eliminate. ull end up with the same results without filling all that table

[@AmirBehtar]

That was the best video I've ever seen in terms of Island Of Liars&Truth Speakers. I just wish you could also go through some more examples in terms of these kinda questions:)

[@saiefshamsmurad8543]

15:56 DON'T INVITE ANYONE!!! Simplest solution ever (assuming that then they won't be "unhappy" with me )

[@ramyhuber8392]

Yes makes it so simple!

[@Carrymejane]

!!!!! 😂

[@csjoy4682]

thanks for your explanation, mam. now, I got understand the idea of logic puzzle. I am a student in computer science and engineering. You got an student. from Bangladesh

[@spencerjames9417]

I wish I could've had you a professor

[@kristoffercorbyn9627]

My preferred approach to the truth table for knights and knaves is by making each column and explicit logical statement that you can plug in the truth values into, all building up to the final conclusion in the last column. Like: (A), (B), (AB), (A XOR B), (B(A XOR B)), [(AB) ^ (B(A XOR B))]. Setting up the biconditionals effectively sorts out the truth of their claims accounting for their state as a knight or knave. That way it's all really straight forward plugging in T/F with no thinking involved.

[@SawFinMath]

I’d love to see what you mean. Feel free to shoot me an email! [e-mail]

[@kristoffercorbyn9627]

Let me try to clarify my original comment, I meant that the following are the column headings of the truth table, separated by commas: "(A), (B), (AB), (A XOR B), (B(A XOR B)), [(AB) ^ (B(A XOR B))] and you let A equal "A is a knight" and B equal "B is a knight". The assessment as to whether their statements is consistent with their characters (as either a knight or a knave) can be expressed in a column as a biconditional of the truth value of their statement with the truth value of themselves (T = Knight, F= Knave). So for example, if A is false and B is false, then AB evaluates to true (i.e. Person A was a knave and he lied). Person B is making the claim that A XOR B, either [A is false and B is true], or [B is true and A is false]. On the truth table it looks like the negation of the truth table of the biconditional AB. So B (A XOR B) evaluates to true only when 1) B is a knight that's telling the truth or 2) when B is a knave that is lying. And forming the conjunction of both (AB) and (B(A XOR B)) in the last column gives you a value of true for all the possible combinations that are logically consistent with their roles. Usually this mean you will get only one true in the last column and it will be on the row with the correct truth values of all persons, in this case when A is F and B is F, they are both knaves because (AB)^(B(A XOR B) evaluates to (True) ^ (True) in that scenario when you plug in the values. It's a lot setup but I like the systematic approach and I am already used to doing truth tables like this where the columns are the parts of the logical statements being made@@SawFinMath

[@joewilliams8658]

@@kristoffercorbyn9627 I just spent a bit of my afternoon evaluating different methods of applying truth tables to knights and knaves problems. I think this is the most explicit and comprehensive method because it's the only way I came across which isolates truth-values to the cells of the table - other methods encode biconditional statements into the cells with additional markings (ticks and crosses, or elimination of rows). Thank you for the clear explanation.

[@Pg_Tobby]

for real that possible actually expanded my range of thinking...thanks alot

[@meepsalotmeepditor3806]

im at my freshman yeah learning DM for software engineering, i couldnt understand my professor well , but thanks to your course im slowly getting the hang of it, your courses are amazing !

[@taekwondotime]

TIP: The truth table at 13:00 is much easier to construct and solve if you just put the following six columns: j, s, k, j->s', s->k, k->j. 1.) Put all possible combinations of T/F for each of j, s, and k columns. 2.) Then evaluate the three conditional statements for each possible outcome as T/F. 3.) The solution then, is the rows where all three conditional statements are true (T). Example: j s k j->s' s->k k->j T T T F T T T T F F F T T F T T T T (valid) T F F T T T (valid) F T T T T F F T F T F T F F T T T F F F F T T T

[@sunnyzhu5791]

American will be great again. Before that, everyone should come here to learn from professor Kimberly Brehm

[@buh357]

Yes, I finally understood this lecture. Thank you,🥰.

[@u12blue]

The second example is confusing especially if you interchange the sentence structure on where the "if" is located. 1 and 2 supposed to be constructed differently yet they share are having the same conditional structure

[@colonelh.s.l.3834]

Solid explanation. I am so bad at logic, but this is helping! However, quick question: in the beginning, why do you do combinations of p ^ q? Why is it specifically "and"?

[@KnowledgeIsGold]

Would like to know this too

[@RobertoRodriguez-nf4ys]

Because you can only determine the types of A and B after considering what they BOTH have to say about each other. An "or" proposition in the first case, for example, where you assume both A and B are knights, would be true, since you would only need to hear A say that B is a knight.

[@coderide]

Thanks!

[@SawFinMath]

Thanks so much for the super thanks! Sorry, this was a while ago. I didn't see the notification.

[@coderide]

​@@SawFinMath No problem ma'am, I know its not much :) but it's what I could give from heart :)

[@sunnyzhu5791]

This video is excellent. But from 9:17, I do not understand, could you give us more detail? Thank you.

[@SawFinMath]

Do you not understand the question or how I set up the table?

[@sunnyzhu5791]

@@SawFinMath I understand the question. But I do not understand how did you solve the question step by step.

[@sunnyzhu5791]

@@SawFinMath, I reference others videos and books. I can not find the answers to this question

[@horsepower33]

these logic puzzles have me feeling so stupid... and i simply would not Invite Jasmine, Samir or Kanti. Update: No disrespect to Professor B. But this video helped me to understand logic puzzles, especially this one we are doing, much better: kzbin.info/www/bejne/rF7GZ3WubNasbLM . I believe its because i can see the terms Knights and Knaves that it made much more sense to me. Also to remember that knights always tell the truth and knaves always lie. Now I can proceed to Discrete Math - 1.2.3 Introduction to Logic Circuits :).

[@SawFinMath]

Agreed. I should have named one of them Karen 😁

[@buh357]

The video you shared helped me to understand the puzzle. Thank you.

[@sabby8093]

Thanks, really love your videos, it helped me to pass the examination.

[@RenaudAlly]

Commenting here so I can hopefully come back to this video. I'm still confused on how to translate sentences to implication propositions (difference between "if" and "only if")

[@dahikaayyub6960]

At 5:20, the teacher says that we automatically assume that p from the second column (A says B is a knight) and q from the third column (B says the two are of opposite types) are going to have the same values as the first column (possibilities). Why? I have watched it again multiple times and I am thoroughly confused. I don't understand why we use the same values. Is there a reason? There's probably something I'm missing. Can someone please help? I'm slowly going insane.

[@oljekiii134]

Im not sure if this will help you but this helped me. A is represented as P and B is represented as Q. So in 2nd column (A says "B " is a Knight") we put all T/F values of P from first column into P in second column as remember its about what A says and A is represented as P. Third column is about what B says. As we know B is represented as Q, we put all the Q T/F values from first column into the 3rd column for Q.

[@akira9195]

that sound effect was totally necessary😂

[@p0intblAnkwaziT]

Hi Prof. Brehm, in your actual discrete math course, do you assign logic puzzles, like the ones covered in this video, for exams? I bought the textbook and student solution manual; I'm using this to self-teach the material and I want to make sure I'm not going too easy or too hard on myself - thanks!

[@SawFinMath]

I believe I assign one or two to homework and then one as an extra credit on an assessment.

[@p0intblAnkwaziT]

@@SawFinMath Thank you for the fast reply prof!

[@fatinkazi8132]

hi can you suggest which video may really help for the first year of computer science as I am kind of preparing

[@SawFinMath]

This whole course is a great introduction to computer science. You won't need the proofs, but the content is important.

[@roblox21242]

I got very confused with the knight one, can someone explain why the last one is correct? I got lost with everything to be honest.

[@GD-Display]

Yeah I was confused too but so basically the last part says p is not true and q is not true. So u have to prove whether that’s correct or not. If that statement is correct then u have ur answer. A is a knight according to p, but since p is being negated, a is not a knight. So he’s a knave. And knaves lie. Not q means b is not a knight. So if a is lying like I said claiming that b is a knight, then a is still lying. Therefore making b a knave. So since b is a knave, he’s going to lie too, since knaves always lie. So if b says “we are opposite types”, is he telling the truth? No. Why? It’s because b is a knave and knaves always lie, therefore making both a and b being knaves. So they are not opposites. U see how that adds up? That means a and b are both lying just like how the original statement says, “p isn’t true and q isn’t true”. Let me know if this helps.

[@failure795]

i dont understand 2:47

[@FakhrulIslamRatul]

I solved the knight and knave puzzle like this: Let x be the proposition for A's statement and y be the proposition for B's statement. According to the question, p ⇒ x, x ⇒ q, q ⇒ y, y ⇒ p ⊕ q, therefore, p ⇒ ¬q But we saw, p ⇒ x, x ⇒ q, So, p ⇒ q, which contradicts our earlier assumption. Therefore, p is not true. So, A is a knave. Now, ¬p ⇒ ¬x ¬x ⇒ ¬q So, B is also a knave. Is my answer and sequence of logics are correct?

[@annoyingprecision2487]

Professor Brehm! Do you suggest reading the textbook first and follow it up with your lecture or do you recommend reversing the order? Thank you.

[@SawFinMath]

Purely personal choice. I have students that do it each way. For my personal learning style, I would watch the videos first because I don't learn math well by reading. But others who do may want to read first.

[@annoyingprecision2487]

@@SawFinMath Thank you.

[@roblox21242]

@@SawFinMath I'm in the same boat as you professor. i'm a visual learn and dont learn well when just reading. your videos have been a life saver for me... but this video im stuck with the knights.

[@humayunbutt555]

In Video 1.2.1 Practice Q2, the term "ONLY IF" ended up reversing the hypothesis and the conclusion. Using that logic, in the above video 1.2.2, for the second example, should we not reverse the implication from S-->K to K-->S due to the use of the "ONLY IF" term - i.e. Samir will attend only if Kanti will be there implies K-->S. In which case, the solutions are (i) Jasmine attends and Samir and Kanti do not, (ii) Samir attends and Jasmine and Kanti do not, and (iii) all three do not attend. On a side note, your lecture videos are of much help and thanks a lot for posting these.

[@charlesadjei4656]

I did what you did based on the previous lesson too but realised I was wrong. In the question, it states Samir will attend only if Kanti attends. Therefore under no circumstance can Samir attend on his own. Your process was correct however, it was our understanding of the second compound proposition that let us down

[@shumayilkhizer1838]

very nicely explained

[@athiambonyabundi]

you are a blessing!

[@syamalchattopadhyay2893]

Outstanding video lecture.

[@GD-Display]

W teacher 🙏

[@curtpiazza1688]

Cool Stuff! 😅 Thanx!

[@charlesadjei4656]

Knights and Knaves question: Why did you copy truth values of p to person A's statement and truth values of q to person B's statement? I understand how you filled the possibilities columns and the column 4 and 6 but not why you set the table as you did. Thank you in advance for your help :)

[@charlesadjei4656]

Did we assign p's truth values to person A because the proposition p is a statement about A and likewise for B? But I guess the deeper question still remains why you assign a proposition about A to what A says?

[@SawFinMath]

I'm not sure I understand the question. Which columns are you referring to?

[@brunilda]

It is just a visual trick to make sure that what indicates that a solution has been found is that the pair of letters (truth-values, actually) in columns 1 & 2, match the pair in 3 & 4, and also in 5 & 6.

[@aishimafrenzy]

I almost lose my mind At the last part I keep focusing on k and be like where did she get the positive that she is writing Thank you so much for the video

[@sugarful5950]

this is harder than Kant philosophy

[@Carrymejane]

Human connection problem!😂

[@emmanuelu]

i wonder if people create truth tables in real life to figure out who and who not to invite

[@SawFinMath]

Only math nerds?

[@ildaraliev1696]

is this discrete math taught in a first year of computer science?

[@SawFinMath]

Yes

[@hrithiksarma2934]

Great

[@darnamism9479]

reminds me of a logic problem from brilliant

[@panpan7782]

so we can "not" invite some of them i thought that if Kanti is coming Samir is 100% coming too becuse he said he will only come if Kanti is there and therefore the only solution i had was to not invite any of them.

[@jamesbondisamonkey]

the party one seems easier as a while loop, where you can basically test for cases until a condition is met, and break from the loop... and never invite people named Samir to parties

[@ulysses_grant]

lol, just like an automata?

[@ulysses_grant]

Dear professor B, I'm still struggling a little with those Knights and Knaves here. I tried to look that (very) same problem up on the internet and I had found this conclusion: A says "B is a knight". If A is a Knight, the statement that B is a Knight is also true. If A were a Knave, the statement would be false. Therefore, we can conclude that A is a Knight. B says "We're both different types". If B is a Knight, the statement is true and implies that A is a Knave. If B were a Knave, the statement would be false, which would mean that both (A and B) are of the same type. But this contradicts the claim that A is a Knight, which we already know to be true. So we cannot have the situation where B is a Knave. So we can conclude that B is also a Knight. Therefore, A is a Knight and B is a Knight. I know this is wrong, but I can't tell why... And I'm deep frying my brains here to try to get to the right answer. But can you shed some light on it and show me where the error is? Thank you so much in advance!

[@ulysses_grant]

Sorry, I think I found the error. It seems to be in the precipitate conclusion "Therefore, we can conclude that A is a Knight". Actually, we cannot conclude that A is a knight, because if we did so, we would be assuming that A is telling the truth. But we still don't have means to prove A is telling the truth yet. Therefore, A can be lying and be a knave. Is that it? Thank you professor!

[@sleepmusicforbabies897]

My good human Samir out here not getting invited in any forseeable circumstance smh 🤦‍♂️

[@SawFinMath]

Haha! You don't want friends like that anyway!

[@juancabrera8181]

this makes no sense to me :(

[@SawFinMath]

They are definitely tough questions!

[@Dopenyc1]

rewatch it again from the beginning and make sure you understand everything she is talking or go back to previews videos so you can catch up on what you might be missing from this vide. Good luck !

[@ntsakomculu371]

These kind of problems require you to rewatch, practice and practice.

[@the.nthaaaa]

@@ntsakomculu371 okay

[@RafaelRabinovich]

On the first puzzle: A is a knave, and his statement "B is a knight" is false, which means that B is also a knave. Then B says that A and B are different kinds, which is also false, since both are knaves. Both statements are false, thus both A and B are knaves. A B A's statement B's statement T T T F T F T T F T F T F F F F

[@holywarriorforthekingdom613]

I agree with some of the other comments. This is difficult to follow and lacks explanation of what you are actually doing.

[@welium123]

I think I'll need a chianti after all these logic puzzles!

[@SawFinMath]

Pour one for me!

[@Dopenyc1]

i love the last possibility grow up butnone of ya are getting invited though

[@SawFinMath]

Agreed!

[@Carrymejane]

I'll comeback here later 😭

[@ntsakomculu371]

Good headache, haha.

[@SawFinMath]

Math always is!

[@sigmatau8231]

... when u need new friends

[@gimbob4975]

Why y'all need these tables, can figure them out from a quick glance.

[@SawFinMath]

Tables are just one way to determine a solution. Most professors require you to either show work or reason through your solution, so this is one way to do that.

[@ridhwan135]

got tricked twice..damn..

[@Nabiile]

poor samir