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)
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.
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
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.
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).
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.
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...
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~
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.
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
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!
In a situation where you would have a double negation through the simplification of a problem similar to the last one you've done, does that double negation law applies to quantifiers/predicates as well or is that to be treated some other way? Thank you!
the last negation you did I don't get it. I don't get it how u got -A. I thought we use the trick you showed us so if I follow the trick it show give me -E for A but for A u got -A. that part I cannot understand. This step is shown around (13:24) min. If anyone of u guys understood the last part then I will appreciate if u help me. thx
Question for "given two rationals x and y, sqrt(xy) will also be rational." apart from your abbreviation, could this also be expressed as (∀x,y∈Q) => (sqrt(xy) ∈ Q)
I have the same question. My guess is yes. "If any two numbers x,y are rational, then sqrt(x,y) is also rational." Sounds like an If, then statement to me.
So if I try to put in a sentence what you did at the end of the video after doing the negation, can I say it as 'is there an x for all y such that not P( x, y ) or not Q( y )
Well, pedantically we should not have "and" between quantifiers and just say "for all x in Q, for all y in Q". We could surely define a comma pretty intuitively if we wanted to.
TheTrevTutor yaa you’re right, practically speaking u'll most likely do it that way.... but i'm just in my first semester in IT study ah i just HAD to say it :D i just love logicc ^^ also thx for the fast answer ^^ have a nice day :)
![[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)
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..
A1 handwriting dude
You are a godsend! My professor only left us with incomplete slides and a textbook that doesn't go into depth on the topic.
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.
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
man u made the damn thing pretty easy. thanx man :)
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.
Dude you are saving my sanity with these videos, thank you so much!
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.
It all makes sense now
that was a great tutorial
you made this so easy for me
with love from INDIA 🇮🇳
These videos are really helpful, thank you very much for coming up with such great ideas
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.
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 )
If you want to get a good grade for the year, listen to this guys steps, he Actually breaks it down step by step,
Love your explanations, always clear. Also just loves listening to you, nice voice and nice handwriting. Thank you for your content 🫶🏻
All of these videos for logic are awesome! Very helpful and well explained! THANK YOU!!!
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.
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...
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~
Cool method to understand the meaning of negation of first order predicate logic.
Such a nice and clear video. Learned a lot.
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.
Good job. It's gonna been great for me to learn more about your study
YOU ARE GOOD IN TEACHING THIS IS SO HELPFUL !
Thank you for sharing this knowledge! It was very helpful!
Negation part is at 6:20
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
Thank you, from the bottom of my heart.
Dude you deserve more subs and likes.
thanks ur videos help a lot in this dire situation..it helped me understand many things that i couldn't do from online class
Can you tell us why our professor is not doing the same? Appreciate it you are a life saver.
You are a great teacher! Thank you so much for creating the videos!
This helped so much. I can't thank you enough!!
very nice explanation..
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 vid. nice job man
You sound like James from Casually Explained
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)?
Thank you for saving my life!
I truly appreciate this.
Your videos have helped so much!
thank you again sir, you are brilliant!
Thank you. My textbook is absolutely hopeless at explaining this stuff.
Thank you so much for making these videos. You make my life easier :D
Thank you man!! Keep up the good work you are educating so many people =)
Very nice explanation
That's crazyy, great lecture mann!
Thank you so much. God bless you.
You are amazing, thank you for such a great lesson
Great help, thanks!
Wow you really nailed it.... thanks
i hope you know that you are an amazing human
this video helped me so much, thank you !
Thank you so much this is very helpful
it is really helped me. thanks a ton
This was an excellent video. No cap
That was so awesome! thanks
It's really good just wish there were harder examples like in 'how to prove it'
Thank you!
Not all heroes wear capes
Agreed
you have a point there
thank u so much ur videos really helped me a lot
Hi There, What tools (board, pen and tablet) are you using for the presentation?
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!
can anyone explain 5:17, i've watched that part over and over but i dont understand it at all.
very well done
In a situation where you would have a double negation through the simplification of a problem similar to the last one you've done, does that double negation law applies to quantifiers/predicates as well or is that to be treated some other way? Thank you!
I lost 10 points on the test for this question, I should watch carefully!
Damn i have my exam on Wednesday 😭
the last negation you did I don't get it. I don't get it how u got -A. I thought we use the trick you showed us so if I follow the trick it show give me -E for A but for A u got -A. that part I cannot understand. This step is shown around (13:24) min. If anyone of u guys understood the last part then I will appreciate if u help me. thx
Thank you man.
awesome...now i understand
Thank you so much !
I really thank for good leason
Nicely done
Why at 8:15 do the and symbols change to or symbols when negated?
DeMorgan's law
Question for "given two rationals x and y, sqrt(xy) will also be rational."
apart from your abbreviation, could this also be expressed as (∀x,y∈Q) => (sqrt(xy) ∈ Q)
I have the same question. My guess is yes. "If any two numbers x,y are rational, then sqrt(x,y) is also rational."
Sounds like an If, then statement to me.
Great video
test on thursday, thank you.
Fsu discrete gang
You're a godsend.
you are the best tnx soooo much
thats clear and useful!
could you please create more videos for theoretical computer science
So if I try to put in a sentence what you did at the end of the video after doing the negation, can I say it as 'is there an x for all y such that not P( x, y ) or not Q( y )
what application are you using to write down ?
Good explanation :)
very useful thanks
good teaching
you got it wrong at 5:32!
there is no comma symbol ever defined. Instead it should read: For All x in Q AND for All y in Q.....
Well, pedantically we should not have "and" between quantifiers and just say "for all x in Q, for all y in Q". We could surely define a comma pretty intuitively if we wanted to.
TheTrevTutor yaa you’re right, practically speaking u'll most likely do it that way.... but i'm just in my first semester in IT study ah i just HAD to say it :D i just love logicc ^^
also thx for the fast answer ^^
have a nice day :)
Thank you!!!
Great stuff
5:02 uh oh We got a mistake over there :)