Knights, Knaves, and Propositional Logic [Discrete Math Class]

This video is not like my normal uploads. This is a supplemental video from one of my courses that I made in case students had to quarantine. I decided that it might be of general interest for people wanting to learn about propositional logic (mathematical propositions, logical connectives - "and", "or", and "not", truth tables, logical equivalence, and the DeMorgan's laws) and one way that they can be used to solve classic Knights and Knaves problems.

Note that this video is part of a series kept in a playlist called [Discrete Math Class]:

If you like this video, consider subscribing to my channel and let me know in the comments if you'd like to see more like this.

This textbook for the course is the open-source textbook by Oscar Levin:
The video investigates ideas from Chapter 0.2 and Chapter 3.1.

0:00 : Knights and Knaves with Truth Tables
00:07 : Introduction with Knight and Knave Problem
00:48 : Propositions and Mathematical Statements
02:20 : Logical connectives and truth tables
05:20 : A detailed truth table example
07:00 : Logical equivalence and the DeMorgan's laws
08:55 : Revisiting the Knights and Knaves problem (solution)
11:30 : A bonus problem

#logic #propositionallogic #truthtables #knights #knaves #logicalconnectives #propositions #math #manim #logicpuzzle #demorgans #demorganslaws

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[mattkriese]

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!

[jakobr_]

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.

[academyofuselessideas]

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

[RandyKing]

great intro to prop logic, i hope you decide to put videos of this type together on a separate channel

[jaiminpatel]

Both are knights and also thank you so much for video. Great Job.

[mathflipped]

This is quite a bit of change of pace compared to the other videos. I also wanted to eventually cover problems of this kind.

[loveyourneighbourasyoursel]

Great Work I hope you will continue your pursuit of truth.

[blankboy-wwjt]

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.

[CapelloYT]

the comparison for what person A and person B said is basically just using the biconditional to determine when both are true right?

[LUMEN_science]

very good. The voice is very good too.

[sheetalgumgol]

9:54, why did we use 'or' disjunction and why not the and conjunction

[Alidaher]

If for the person that said nothing he would be a knight or a knave, can we use that for B said?

[aashsyed]

9:55 how do we find in in general can you do a video on that?