Negating Logical Statements with Multiple Quantifiers
ฝัง
- เผยแพร่เมื่อ 9 ก.ย. 2017
- How do you negate a logical statement that multiple "for all" and "there exist" quantifiers in it?
We've seen previously how to negate a single universal or existential quantifier in the playlist here: • Discrete Math (Full Co...
Now we upgrade to the case of multiple quantifiers. The idea is that every "for all" flips to a "there exist" and vice versa, and the final predicate becomes negated. We will practice interpreting an english sentence as a logical statement with multiple quantifiers, negate it formally, then convert back to english.
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Why TH-cam tutorials always better than school teachers ?
@@amantiwari814 it is.... you study this at university level proof. im doing it right now in my proof and analysis class
Simplest answer they have script
for real
Congratulations on mastering the ability of taking complex subjects and breaking them down into simple concepts that are easy to understand. The world needs more teachers like you. Thankfully, TH-cam exists which allows for all users worldwide to benefit from your superb teaching style.
Wow... can't tell you how much your discrete mathematics videos have helped me
So glad they’re helping!
Best tutorial ever.....
The video is great! I love it!! But there seems to be a loophole in the "Some number in D is the largest" statement. If we look at the "math translated" version of the statement, there exists a domain D, such that these two statements would not be equivalent. eg. D = {1, 1, 1, 1}. The math version would be true, because there exists 1 which is greater or equal then every other element of set D. But the english version would not be, because there isn't a number in the set which is the largest. As I understood it, the property should have contained a negation of x = y, and should have looked something like this: There exists some x in D, such that for all y in D, y ≠ x and x > y.
I also want to thank you for such a great Discrete math course! It's absolutely awesome!
I am honestly kind of a moron and it's been a decade since I last studied college-level math. I went back to school this year and I might be too dumb to grasp discrete math, but these videos give me hope.
Your explanation is so clear! I think if I were your student, you will be my most favourable teacher!
I appreciate this lesson
Perfect! I was scared of those symbols before I watched this video but look at me now.
Helped me understand this topic, thank you so much. I would say to go over some more complex examples and explain it in pure English. Other than that, great video!!!
It feels like I had a lightbulb moment during this video. I love this explaination. I honestly like all of your explination videos so far, but this one if my favorite. Again, thank you and I am forever greateful to you.
You're a legend man, thanks for the help!
offff , finally I found someone who thinks as I do ❤❤❤❤
love from nepal ..best lesson ever
you beast, saved me this day
Great explanation
Thank you so much for this video
Sir you are really good teacher
Thank you bro
You da best
I wish more video like this exists but then universities will go out of business because more people can learn the materials on theirs own without ever have to spend money out of their pockets.
You just saved my life
sir, how do you sync animation with your movement?
you saved my day G
his board is so trippy. like he is writing from behind it and we can everything the right side. and also he can see the text question in real time from his computer on his board. Damn
7:05 > _"for everything _*_else_*_ in the domain"_
small nitpick, i think the else part would require explicilty removing it from domain like D - {x}, in the current form in video, this just means all values in domain (x included); am i right?
this lesson is gooooooood!1!!1!!
Good luck at UVic!
thanks
"Some number in D is the largest", can I use (imho simpler) version something like MAX(x) instead of P(x) ?
Sir u deserve 10m+ subscribers. I hope It will.
sorry sir .......
It is a typing error.....
I mean 10m+ subscribers.
I like the way you teach.
Thank you very much sir.
I have question:
Why is the statement "Every integer has a larger integer" true but it's negation, although expected to be false, doesn't actually seem to be false to me? When prooving the statement ""Every integer has a larger integer", Trefor Bazett says you can take any integer x, add 1 to it and get an integer bigger than x. But when prooving the negation of the same statement, Trefor says "There is just no number out there that is bigger than everything else…", but that contradicts the reasoning used to prove the statement is true. I would be thankful if someone can clarify this a little bit to me.
Its negation is that there exists a number, that every other number is smaller than that number. Is false because integers can keep increasing. There is no number that is bigger than everything because there is always a bigger integer.
@@duwartstewart5639 I get it now. One has to be careful how he reads these statements. Thank you for the answer.
Just out of curiosity, what is the difference between the following statements?
∀x∈D, ∃y∈D, L(y,x) → H(x)
∀x∈D, [∃y∈D, L(y,x)] → H(x)
@@DrTrefor
Thanks.
I wasn't sure if the IF for the first one applied to the whole left side, or just L(y, x)
1:41 1:47 > _"still think of it as a property of x [P(x)]_ ... _because I've quantified my y"_
ahwww, awesome.
yeah, i forgot that a variable/predicate quantified becomes like a constant/statement.
1:41 1:47 > _"still think of it as a property of x_ [P(x)] ... _because I've quantified my y ..."_
ahwww, awesome.
yeah, i forgot this: a predicate quantified becomes a statement.
Are you writing backwards, or did you reverse the video?
im having so much trouble understanding multiple quantifiers in epsilon delta definition of limit
Is he writing all the things backward?
No. The image is flipped. Look at the buttons of his shirt. They are in the "wrong" side for a man.
@@DrTrefor If you compare the buttons of your shirt with that of the female's shirt, then you will understand what is he talking about. But thanks for making such an amazing course.
Which books to use for discrete mathematics , I am bigginer
Here is a good free one: discrete.openmathbooks.org/dmoi3/
@@DrTrefor thank you
I like u sir
Thank you niggation
Your welcome
Kudos to you for writing backwards
nvm i bet it's just flipped around
4:44
isn't infinity the largest integer?
and if it is,
the negated statement would be True as we!!
@@DrTrefor hmm...
Infinity is not an integer, it is a limit.
No. Infinity is an idea, not an actual number. So, it can't be treated as such.
I wish there was a longer statement lolll my teacher put some super long ones on my test and it gets confusing
Honestly longer ones are challenging mostly because there are just symbols everywhere, but they are only doing exactly what we did in this video over and over again
You know what I like about logic? When you flip it and get an absolute nonsense. 4:33
My god this voice. Excellent explanations but I feel like you are yelling this information at me.
How is he writing backwards thats impressive
is he writing backwards?
How do you write on the board? Are you writing backward? if yes you are my god man😂
Saviour. XD
1:06 "bigger than my x"
when you dont have a largest number then you also domt have a smallest numcer
1:41 1:47 > _"still think of it as a property of x [P(x)]_ ... _because I've quantified my y"_
ahwww, awesome.
yeah, i forgot that a variable/predicate quantified becomes like a constant/statement.