PREDICATE LOGIC and QUANTIFIER NEGATION - DISCRETE MATHEMATICS
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- เผยแพร่เมื่อ 16 ก.ค. 2017
- Today we wrap up our discussion of logic by introduction quantificational logic. This includes talking about existence and universality. We also discuss the negation of our quantificational operators.
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Discrete Mathematics 1: • Discrete Math (Sets, L...
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Discrete and Combinatorial Mathematics (Grimaldi): amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): amzn.to/3lUgrMI
Book of Proof (Hammack): amzn.to/35eEbVg
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![[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](/img/n.gif)
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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.
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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!
Cool method to understand the meaning of negation of first order predicate logic.
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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
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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 )
Hi There, What tools (board, pen and tablet) are you using for the presentation?
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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)
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Great tuts! But what about infinity? Domain is not finite? When for example we have "exists for all x\in Real number" P(x) is true P(1) or P(2) or ... so. Please give some explanation because you show definition for finite domain..I think.
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.
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.
Help professor,this doubt is eating me up for days,
Does dog refers to class/group of all animals satisfying dog properties or refers to every individual satisfying dog conditions
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Shouldn't there be for some x "such that" instead of a comma
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can you please help me out with this one bc I have no idea how to write this one out?
Department (D-code, D-Name, Chair-SSN)
Course (D-code, C-no, Title, Units)
Prereq (D-code, C-no, P-code, P-no)
Class (Class-no, D-code, C-no, Instructor-SSN)
Faculty (SSN, F-Name, D-Code, Rank)
Student (Ssn, S-Name, Major, Status)
Enrollment (Class-no, Student-Ssn)
Transcript (Student-Ssn, D-Code, C-no, Grade)
Courses with C-no between 300 and 399 must have at least one prerequisites; and
courses with C-no between 400 and 499 must have at least two prerequisites
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.
Thank you
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.
Life saver
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