[Discrete Mathematics] Negating Quantifiers and Translation Examples

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In this video, we translate English sentences into quantificational logic and then negate some quantificational statements.

Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[Trevtutor]

It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!

[eman]

Thank you for your very clear examples!

[abiokpobatubo]

Thank you for your videos even after 6 years. I have a question, please how do you negate “For every strictly positive epsilon there exists a strictly positive delta such that |f(x)| < e (epsilon) whenever |x| < delta ?

[ROCLife]

In the last exercise, how did you go from Ex [ - (Px -> Qx) ] to Ex [ -(-Px v Qx) ] "-" denotes "not" and "E" denotes "there exists"?

[ES]

Hi, I hate taking notes on paper, what note taking software are you using to make this video? I'm currently using my stylus/wacom tablet but the drawing software that comes with it is wayyyy more than I need to just take notes.

[nightravels]

A little confused here. In the previous video we learnt that ∃xPx <=> ~Vx[~P(x)]

So why is the first negation example in this video showing that ∃x (Px ^ Qx) <=> Vx (~P(x) v ~Q(x)?

Shouldn't the V quantifier have a ~ in front of it? I also tried applying the trick you showed in the previous video to negate quantifiers, and it gave me ~Vx (~Px v ~Qx )

If anybody could clear this up it would be greatly appreciated

[lubababazlulmoon]

Consider the compound proposition (Allm∃n [P(m, n)]implies( ∃nAllm[P(m, n)]) where both m and n are integers. Determine
the truth value of the proposition if
(a) P(m, n) is the statement “m < n”.
(b) P(m, n) is the statement “m | n”. [By “m | n”,
which we say as “m divides n”, we mean that n = km for some integer k.]
how to do these? And it will be a great help if you make a video with similar problems like these.

[birdt]

5:16
Q:- Write a nontrivial negation:
- Between any integer and any larger integer, there is a real number.
What the solution???

[mitchyemmen]

Isn't the second case at 2:06 incorrect? if x were to be -5 and y were to be -3/ 25 is >9 but -5 is not > -3.

[johanronkko]

If i have some predicate so that it's statement is considered to be false, when i negate it does it become true? Is that how it works?

[mohamedasim]

Why is it for all x (s(x) arrow m(x) or c(x))?
Is it supposed to be for all x (m(x) or c(x))?
My question is on the first sentence of translation

[mubarizmirzayev]

Hi, firstly thanks for this beneficial video :) My question is where did we know that (Px -> Qx) = ~Px v Qx, Thanks beforehand :)

[saifchannel]

Hi mate,


can u help me on this?
1. a) Consider the statement:
For every integer x and every integer y there is an integer n such that
if then .
i. Translate the statement into symbols. Clearly state which statement is the proposition p and which is the proposition q, the quantifiers and the connectives.

[mihailmojsoski]

4:16 that looks like a C function pointer a little

[marvinbadilla]

Why didn't you negate all your quantifiers as example? It would be so helpful

[anlberkearslantas]

does any one know why he did add "-" at 3:51

[mbarq]

@5:09, you meant "There is some number that is odd AND even", right?? since that's what [∃x(Px＾Qx)] translates to, no? Then you negate it to "There is not a single number that is odd or even", or ¬[∃x(Px＾Qx)]

[manjitshakya]

Express this statement using quantifiers:
“Every student in this class has taken some course in every department in the school of mathematical sciences.”

[JROD]

What does any of this even mean?

Were you even speaking English?