Discrete Math - 1.5.2 Translating with Nested Quantifiers

[@2251230]

If there is a nobel prize for teaching, you deserve it. thx u for making my life so much easier.

[@tanhnguyen2025]

don't flatter her up. What she taught u in these videos were just merely the tip of the iceberg. Deep down, there's a lot of stuff u miss out on by watching these videos and in order to have a deep understanding u gotta learn from the original textbook where they show you detailed minutiae of the concepts and give you hands-on problems

[@Louay-l6e]

a good textbook?? ​@@tanhnguyen2025

[@t.o.g.thatoneguy5130]

@tanhnguyen2025 🤓 ^ "urmh actualy dont flatter her even though I couldn't do an 80 part lecture series on this I can read the book and master the way of discrete math better than you peasants" get a life bozo

[@Xxx_Peyton_xxX]

@@tanhnguyen2025 shut up nerd

[@habib_khan]

I can't thank you enough Professor. The entire playlist is literally a gold mine for students taking DM. I've shared it to my classmates and everyone love your videos. Thank you for making this course easy for us. You're an absolute gem!

[@SawFinMath]

Thanks so much! Glad they help, and thanks for sharing!

[@habib_khan]

@@SawFinMath 🤍✨

[@valeriereid2337]

Thank you Professor Brehm I will remember you as the person who got me to understand logic.

[@theshadeofdunwall]

really helpful videos. good pacing, clear instruction and the right concepts are explained without getting too complicated

[@coolkaw4497]

it seems that more brain power is required in this lesson compared to the ones before. I am starting to have to pause and think for a good minute or two for each question now! All of the variables and propositions can be quite overwhelming at first glance. Thanks for going through each and every step

[@LamNguyen-nm1fq]

Thank you for your video. I've a hard time trying to learn discrete math until I found your channel.

[@lindadeng3149]

I have a question for 15:59. Isn't z present for all of the classes at BN? For both x,y has taken all of the classes?

[@FirebirdGG]

yes it indicates that students x and y are enrolled in exactly the same classes at BU. Not Just One Class: If it were intended to refer to a single class, the expression would typically not include the ∀z quantifier. Instead, it would specify a particular class directly (e.g., S(x,c) and S(y,c) for some specific class c)

[@maryameslam3782]

many thanks from an Artificial intelligence major student from Egypt, God bless you

[@SawFinMath]

Glad I could help! I didn't know than AI majors needed Discrete :)

[@maryameslam3782]

@@SawFinMath it’s super important for us to understand machine learning algorithms so yea any computer scientist need discrete mathematics

[@wintutorials2282]

Omg I don’t know how to thank you for these video❤❤❤❤

[@rchimedes]

At 14:40, I thought y was a class? Why is it now being considered a student?

[@chrisgriswold407]

As far as I can tell, this is simply a poor choice of variable names but is otherwise correct. The names given to the variables in the function declaration "S(x,y)" have no bearing on how it is called. All that matters is that you have a function S that takes two parameters, a student and a class in that order. So, down at the bottom when she is calling the function is when she is making the determination that x and y are students and z is a class. I think it would have been a lot less confusing if she would have just used different letters for the declaration, such as "P(s,c)".

[@PainRUify]

At 18:00, can the answer be ExVy(p(x,y) where P(x): x has taken a flight on airline y ? Thanks!

[@karanveersingh5535]

Thats what I thought , but is it true. Hoping u know it after 1 year.🧐

[@zhuziyuan4141]

what you have shown is that there is a man who has taken all flights.

[@maryl8614]

That's what I got, too, with a slight modification: P(x): x has flown on airline y. I feel like this should work, unless the original problem is stating that the man has only take 1 flight (and only 1 flight) per airline?

[@EA_47_]

Thats my solution too sort off. My solution: P(x,y) denotes " x has taken a flight on airline y" x is all men in the world y is all airlines in the world ∃x ∀y P(x,y)

[@EA_47_]

@@zhuziyuan4141 not true the he denoted that "x has taken a flight on airline y" which only identifies at least one flight

[@ubk42]

Nice video. Just letting you know there is an unmatched parenthesis at 8:30

[@TheBanana821]

Wait, i thought at 14:28 y is a class not another student

[@mutumbakalumba]

that's what i was also thinking

[@pcake4603]

It doesn't matter what you name the variables, it just matters where you place it in the function. y was placed in the first position of the function, so it's treated as a student. This is also why z is treated as a class even though it wasn't in the function.

[@pcake4603]

@@mutumbakalumba Don't treat the variables in the function as the same variables in the propositions. S(x,y) really means S(student, class).

[@danielroh4543]

My professor hardly teaches but your videos are so easy to understand, so thank you! The incomplete parentheses are bothering me though lol

[@edf5927]

I think there's a mistake at around 12:00. The translation is that y is "another student" but there's nothing in the symbolization that says x does not equal y. So the symbolization leaves open the possibility that x and y are the same, so it should be translated without saying "another".

[@Andres-nn5it]

This is not the case because of the or statement. If the proposition T(x) is not true then that student does not use tiktok and therefor cannot be the other student which is a friend to themselves that uses tiktok, and as a result this friend must be another student.

[@edf5927]

What if x is true and x and y referred to the same student? There's nothing in the symbolization to prevent that. @@Andres-nn5it

[@Andres-nn5it]

@@edf5927 if T(x) is true then that person uses tiktok when moving to the second term separated by the or statement of y equals x this implies that they are friends with themselves and they use tiktok which could be argued to be true(they know someone who uses tiktok). Even if it is argued to be false this doesn’t change the truth value it meaning that applies to the whole since it is an or statement and T(x) as stated is already true. If T(x) is true then the entire proposition is true. If we were to then assume x=y and say for the second sub-proposition that this is false (that you can’t be friends with yourself even though it holds true that person x=y does use tik tok) this has no effect on the overall truth value of the overall proposition (since it is a disjunction). So it can be seen that to say that the proposition provided by the professor is equivalent to the same proposition with the notation that adds the limitation x=\ y is in fact a tautology. The proposition you’re advocating for and the proposition provided by the professor have the exact same truth value. If need be you can construct a truth table. Basically the notation isn’t needed we don’t have to prevent x=y.

[@edf5927]

OK, got it.

[@edf5927]

Please see my comment on video 1.8.2. Any thoughts?

[@Gottastudyhard-m3b]

@15:36 Does For-all (z) mean from all of the students in the class, such that x and y are not same students such that student X is taking the same class as student Y?

[@whistlingwind5900]

It seems to me that at 15:50,∀z should represent all BU classes. My full interpretation would have been: If one student has taken all BU classes it is necessary and sufficient for another student to have also taken all BU classes.

[@听音乐-o9j]

The question at 18:00 is so confusing.. lists of quantifiers

[@DONdayce]

If there exists an airline with all flights, how can there be a negating predicate that states that an airline doesn't have a flight when the quantifier states otherwise???

[@davehlave8530]

6:42, for the first question, can I say For All x There Exists y E(x,y) ?

[@Yazan_Majdalawi]

At 7:45 I have put it like this: Ax Ey (...) _with the letters flipped of course _ is my solution still valid?

[@red-sv2qf]

At 15:46, what's the purpose of Az then?

[@FirebirdGG]

Same Classes Enrollment: The use of ∀z establishes that x and y have identical enrollment records across all classes at BU. If this quantifier were absent, the statement would not necessarily indicate that all their classes are the same. so the key point is its Not Just One Class If it were intended to refer to a single class, the expression would typically not include the ∀z quantifier. Instead, it would specify a particular class directly (e.g., S(x,c) and S(y,c) for some specific class c)

[@imboss5544]

9:01 question b, i think the "if..then" statement should be replaced by the "and" statement in the predicate logic

[@shallowfalcon]

So when you define the domain of the function does that apply to the y as well? Because you said y was another student

[@laladuggi]

For question A. at 6:40 can I put Vx E! y E(x,y) and take Joe's name out of the equation ?

[@SawFinMath]

Because the question specifically references Joe, you must use Joe in the prepositional phrase

[@laladuggi]

@@SawFinMath Oh okay that makes sense. So there’s no need to use the uniqueness quantifier or any other because we are assigning the variable y the value Joe?

[@sagivalia5041]

So when I try to translate a sentence to a quantifier, the variables are gonna be what are considered "entities" in the sentence? man, flight, airline?

[@SawFinMath]

Exactly!

[@parsasamandi569]

Thanks for it

[@tobito4397]

is the negation of U the upside down U, "intersection"? Sorry I am new to this concept

[@vade248721]

Example b. In the beginning of the video, are the students sending or receiving the text and email? Your answer says "sent a text" but the problem states "received a text" and "received an email".

[@imboss5544]

y receive an email from x equal to x send an email to y

[@rutchlyngo1324]

Thank you so much😍😍💕

[@shashankvashishtha4454]

thanks for saving me from bad result.

[@FreddSviat]

If only we had such a professor just like you in Poland, students would benefit more being taught by you rather than our Polish professors in Poznan. Thanks for all the explanations!

[@mrrobot-ek8zk]

thank u so much

[@-Mohamed_bayan]

Thank you :)

[@aladin2591]

Shouldn’t be the assertion: “x has taken flight f” rather than “x has taken flight y”!

[@ekemm]

13:00

[@vade248721]

P(x) = taken every flight in the world Domain = all people in the world 3xP(x)

[@normalcrazer1930]

thats what im saying, she just lost me when she wrote bunch of things that dont make sense

[@chhangsrengp5360]

That's wrong. The statement is "taken a flight," meaning it is only 1 flight. Not all the flights of all airlines. but at least 1 flight of all airline.

[@chhangsrengp5360]

@@normalcrazer1930 read my cmt.

[@aru4115]

12:36

[@asura9161]

Our professor doesnt teach and just links your videos lol

[@SawFinMath]

@@asura9161 Hah no fair! I should get some of his salary!

[@GD-Display]

Wth is MA315???? 😭

[@SawFinMath]

The class Discrete Mathematics where I teach

[@GD-Display]

@ no I’m sorry I read the question wrong. I thought it said class y was the domain. Ty tho this series helped me a lot

[@KatherineFix]

Ma brainnnnn🤕😖

[@NicolasFioriniA]

Another note about the students one where ∃x∃y∀x ((x!=y) ^ (S(x,z) ⇔ S(y,z))) I think this could also mean they haven't taken the same class too. Since S(x,z) ⇔ S(y,z) is true when both are false. So x didn't take z and y didn't take z.

[@bigpapaxx3885]

the last Demorgan law you did is incorrect, it is (∀x∀y∃z(¬p(x,y)∧Q(y,z))

[@pcake4603]

Can you explain how? The video seems right to me.

[@beksaylor]

Am I the only one who sends themself an email?

[@RS-xu1dm]

This is all nonsense to me :(

[@SawFinMath]

Start at video 1.

[@RS-xu1dm]

@@SawFinMath Yes, I have been watching them all... I thank you for all the videos, You are a savior. Its just that I got lost watching this one.

[@faceless4759]

I think this video must be the 13th

[@SawFinMath]

Nope. The 13th is an intro to nested quantifiers

[@angadsingh6478]

at 18:00 can I bring the ∃f in front of ⩑a?