Check out my new course in Predicate Logic: trevtutor.com/p/master-discrete-mathematics-predicate-logic It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!
More easy way to derive the formulas: For quantifiers: ¬∀x ∃x 1. Multiplying with "not" both ways (like multiplying with minus both ways): ¬¬∀x ¬∃x ∀x ¬∃x 2. For function just multiply the not: ¬(P(x)) ¬P(x) So for example: ∀x P(x) Do distribution of not: ¬(∀x P(x)) Like multiplying (with not in out case): ¬∀x ¬P(x) Using 1. : ∃x ¬P(x)
I'm a latin young and is amazing your explaning form, currently don't speak english very well, but i can understand you clearly, just this trimester i'm taking discrete mathematics! I'm studying BS in Mathematics
You are honestly an explanation god!! I found your videos a few months ago and they literally saved me. You explained Predicate Logic soo well and easily. I appreciate it a lot. The fact that I get so excited when I know that you have already covered a topic that we cover at Uni and that I get to see your videos on that specific topic is crazy haha.
Stumbling across my fifth Discrete Math course and finally someone cares enough to actually explain the backwards E. There are way too many bad Discrete Math courses out there. This is a godsend.
I used to struggle with negation until I heard "Not all dogs are brown". I used that same example for every other negation, now it's all intuitive. Thanks a lot, man.
What a great video! what you are doing is helping me so much ! I have to study online without having online lecture or explanation and only having scripts of the lecture after the course.
Man thank you, we have a fresh grad mechanical engineer as a professor for this subject with no teaching experience. The exams have been hell. Much appreciated man~
How is that possible : Consider:A is the universal quantifier and E is the existential quantifier and this notation as prime(*) Negation of AxP(x) is *Ex*P(x). On the other hand, when it comes to the question in the 13:25 Consider R(x,y) is the propositons in the brackets. So shouldn't be the negation of Ax[EyR(x,y)] ==> *Ex*Ay*R(x,y) corresponding to the rule above. Because we can consider P(x) as EyR(x,y) so that will be *Ex*[EyR(x,y)] and if we continue in the same way we get *Ex*Ax*R(x,y).
Very helpful, but have one question. On the last problem, why didn't the quantifiers flipped and negated like the four practice problems before? Thanks
If anyone was wondering about 12:22, -I believe that's "not possibly P" being equivalent to "necessarily not P."- I could have it mixed up though, in which case it's "not necessarily P" being equivalent to "possibly not P." EDIT: I mixed it up...
10:21 Correct me if I'm wrong. All dogs are brown. There is not a dog which is not brown. There is a dog which is brown. Not all dogs are not brown / of different colour than brown. Not all dogs brown. There is a dog which is not brown. There is not a dog which is brown. All dogs are not brown / of different colour than brown.
Negation is negation. Equivalence is equivalence. Equivalence is like saying p ~~p, which is what the +/- example was. Negation is negation. Not claiming that p ~p.
Loving this series! Just a minor error: at 4:20 m must belong to the set of complex numbers or your statement becomes a contradiction. For example, if n = -1, m = sqrt(-1) satisfies the equation m^2 = n. As shown, n is a real number while m is a complex number. Again, this is a super minor error, but overall I'm really appreciating your lectures! Kudos to you, TheTrevTutor :)
Counter-example about sqrt(xy).... let x=1/2, y=1/3 .... sqrt(1/2*1/3)=1/[sqrt(2)*sqrt(3)] i.e. the output cannot be represented in the form a/b where a and b are integers, and thus is not a rational number. Only certain rational {x,y} pairs generate rational sqrt(xy) values. Sorry for being a downer, I swear I love your videos!
![[Discrete Mathematics] Negating Quantifiers and Translation Examples](http://i.ytimg.com/vi/7HvCgm4vBv4/mqdefault.jpg)
![[Discrete Mathematics] Negating Quantifiers and Translation Examples](/img/tr.png)
![[Logic] Predicate Logic](http://i.ytimg.com/vi/h5UTvdcgFHw/mqdefault.jpg)
![[#2024MAMA] ROSÉ (로제), Bruno Mars - APT. | Mnet 241122 방송](http://i.ytimg.com/vi/dgGqD28J6aQ/mqdefault.jpg)
Check out my new course in Predicate Logic: trevtutor.com/p/master-discrete-mathematics-predicate-logic
It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!
You are hands down THE best youtube tutor I have ever come across. Great job! May you find yourself rewarded in ten fold.
More easy way to derive the formulas:
For quantifiers:
¬∀x ∃x 1.
Multiplying with "not" both ways (like multiplying with minus both ways): ¬¬∀x ¬∃x
∀x ¬∃x 2.
For function just multiply the not:
¬(P(x)) ¬P(x)
So for example:
∀x P(x)
Do distribution of not:
¬(∀x P(x))
Like multiplying (with not in out case):
¬∀x ¬P(x)
Using 1. :
∃x ¬P(x)
this topic can"t be so easy without this explanation..
You are a godsend! My professor only left us with incomplete slides and a textbook that doesn't go into depth on the topic.
A1 handwriting dude
I'm a latin young and is amazing your explaning form, currently don't speak english very well, but i can understand you clearly, just this trimester i'm taking discrete mathematics! I'm studying BS in Mathematics
You are honestly an explanation god!! I found your videos a few months ago and they literally saved me. You explained Predicate Logic soo well and easily. I appreciate it a lot. The fact that I get so excited when I know that you have already covered a topic that we cover at Uni and that I get to see your videos on that specific topic is crazy haha.
Thank you man .Now I understand the concept of propositional logic,predicate logic and quantifiers.GOD bless you.
Nice videos man, you do a fine job teaching discrete math.
Stumbling across my fifth Discrete Math course and finally someone cares enough to actually explain the backwards E. There are way too many bad Discrete Math courses out there. This is a godsend.
im gonna shove that negation through like it aint nobodies business. Thanks for the tutoring T.
Wish I could up vote this video unlimited times - you are a boss at explaining everything
Boom, I finally get it after this video versus reading the text and university provided references.
If you want to get a good grade for the year, listen to this guys steps, he Actually breaks it down step by step,
man u made the damn thing pretty easy. thanx man :)
I used to struggle with negation until I heard "Not all dogs are brown". I used that same example for every other negation, now it's all intuitive. Thanks a lot, man.
that was a great tutorial
you made this so easy for me
with love from INDIA 🇮🇳
I am teaching this subject this semester and your video helped me to better explain the topic. Thanks!
I want to say that you are the best teacher on Earth, thanks to you I can pass this exam )
Dude you are saving my sanity with these videos, thank you so much!
It all makes sense now
Love your explanations, always clear. Also just loves listening to you, nice voice and nice handwriting. Thank you for your content 🫶🏻
Can you tell us why our professor is not doing the same? Appreciate it you are a life saver.
These videos are really helpful, thank you very much for coming up with such great ideas
Cool method to understand the meaning of negation of first order predicate logic.
What a great video! what you are doing is helping me so much !
I have to study online without having online lecture or explanation and only having scripts of the lecture after the course.
Man thank you, we have a fresh grad mechanical engineer as a professor for this subject with no teaching experience. The exams have been hell. Much appreciated man~
thanks ur videos help a lot in this dire situation..it helped me understand many things that i couldn't do from online class
Good job. It's gonna been great for me to learn more about your study
Thank you, from the bottom of my heart.
Thank you. My textbook is absolutely hopeless at explaining this stuff.
All of these videos for logic are awesome! Very helpful and well explained! THANK YOU!!!
YOU ARE GOOD IN TEACHING THIS IS SO HELPFUL !
Such a nice and clear video. Learned a lot.
You sound like James from Casually Explained
Dude you deserve more subs and likes.
Thank you for sharing this knowledge! It was very helpful!
great vid. nice job man
Thank you for saving my life!
How is that possible :
Consider:A is the universal quantifier and E is the existential quantifier and this notation as prime(*)
Negation of AxP(x) is *Ex*P(x).
On the other hand, when it comes to the question in the 13:25
Consider R(x,y) is the propositons in the brackets.
So shouldn't be the negation of Ax[EyR(x,y)] ==> *Ex*Ay*R(x,y) corresponding to the rule above.
Because we can consider P(x) as EyR(x,y) so that will be *Ex*[EyR(x,y)] and if we continue in the same way we get *Ex*Ax*R(x,y).
The negation of AxP(x) is Ex*P(x), what you stated was a logical equivalence.
You are a great teacher! Thank you so much for creating the videos!
Thank you so much. God bless you.
I truly appreciate this.
very nice explanation..
Very helpful, but have one question. On the last problem, why didn't the quantifiers flipped and negated like the four practice problems before? Thanks
Not all heroes wear capes
Agreed
you have a point there
i hope you know that you are an amazing human
Thank you so much this is very helpful
thank you again sir, you are brilliant!
This helped so much. I can't thank you enough!!
Your videos have helped so much!
Great help, thanks!
Thank you!
Negation part is at 6:20
Very nice explanation
it is really helped me. thanks a ton
Thank you so much for making these videos. You make my life easier :D
thank u so much ur videos really helped me a lot
That's crazyy, great lecture mann!
It's really good just wish there were harder examples like in 'how to prove it'
very well done
Thank you man.
This was an excellent video. No cap
you are the best tnx soooo much
I really thank for good leason
That was so awesome! thanks
If anyone was wondering about 12:22, -I believe that's "not possibly P" being equivalent to "necessarily not P."- I could have it mixed up though, in which case it's "not necessarily P" being equivalent to "possibly not P."
EDIT: I mixed it up...
You are amazing, thank you for such a great lesson
Wow you really nailed it.... thanks
Thank you man!! Keep up the good work you are educating so many people =)
could you please create more videos for theoretical computer science
Great video
At the time of 12:05 in this video, whether do you want to say ~((Exist) X p(X))?Should be the result (All) X ~P(X)?
this video helped me so much, thank you !
Thank you so much !
Life saver
You're a godsend.
Nicely done
thanks
10:21 Correct me if I'm wrong.
All dogs are brown. There is not a dog which is not brown.
There is a dog which is brown. Not all dogs are not brown / of different colour than brown.
Not all dogs brown. There is a dog which is not brown.
There is not a dog which is brown. All dogs are not brown / of different colour than brown.
Thank you!!!
very useful thanks
You the best
Good bro..ths..
thats clear and useful!
awesome...now i understand
test on thursday, thank you.
Fsu discrete gang
its really awesome
I lost 10 points on the test for this question, I should watch carefully!
Damn i have my exam on Wednesday 😭
good teaching
GOD BLESS YOU SIR!!
I'm super confused, why don't you do the + and - for 14:40? Shouldn't it be -Ex - Ay - P(x)? Or is the equivalence different then negating
Negation is negation. Equivalence is equivalence.
Equivalence is like saying p ~~p, which is what the +/- example was.
Negation is negation. Not claiming that p ~p.
Great stuff
I Loooveee you, and thank you !
God bless you
thank you
Loving this series! Just a minor error: at 4:20 m must belong to the set of complex numbers or your statement becomes a contradiction. For example, if n = -1, m = sqrt(-1) satisfies the equation m^2 = n. As shown, n is a real number while m is a complex number. Again, this is a super minor error, but overall I'm really appreciating your lectures! Kudos to you, TheTrevTutor :)
Counter-example about sqrt(xy).... let x=1/2, y=1/3 .... sqrt(1/2*1/3)=1/[sqrt(2)*sqrt(3)] i.e. the output cannot be represented in the form a/b where a and b are integers, and thus is not a rational number. Only certain rational {x,y} pairs generate rational sqrt(xy) values. Sorry for being a downer, I swear I love your videos!
Thx dawg
GOD bless you