Negating Logical Statements with Multiple Quantifiers

How do you negate a logical statement that multiple "for all" and "there exist" quantifiers in it?
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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[karenl]

Why Youtube tutorials always better than school teachers ?

[MULTIFACEPLANTER]

Wow... can't tell you how much your discrete mathematics videos have helped me

[mountaindew]

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.

[matthewrister]

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, YouTube exists which allows for all users worldwide to benefit from your superb teaching style.

[kupinaa]

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!

[mrmeme]

offff, finally I found someone who thinks as I do ❤❤❤❤

[Forkythechanter]

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.

[mohamedrashad]

Perfect! I was scared of those symbols before I watched this video but look at me now.

[AbhishekBade]

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

[SaidVSMath]

You're a legend man, thanks for the help!

[alejandrodavidrodriguez]

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!!!

[amantiwari]

Which books to use for discrete mathematics, I am bigginer

[yash]

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.

[yash]

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.

[thomaslu]

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)

[truthphilic]

sir, how do you sync animation with your movement?

[xuepingsong]

im having so much trouble understanding multiple quantifiers in epsilon delta definition of limit

[kriskanchi]

I wish there was a longer statement lolll my teacher put some super long ones on my test and it gets confusing

[VictorZamanian]

My god this voice. Excellent explanations but I feel like you are yelling this information at me.

[hamdimohammed]

You know what I like about logic? When you flip it and get an absolute nonsense. 4:33