DM JNTUH R18 | Predicates & Quantifiers | Discrete Mathematics | @ramareddymathsacademy

00:17:44
https://www.youtube.com/watch?v=BmdFXpfvync

概要

TLDRLo video de l'acadèmia Ramadin en matemàticas barreja las basas de la logica de predicats, partint de concèptes coma l'equivaléncia logica e las taulas de veritat per explicar predicats e quantificators universals e existencials. Los predicats, dins lo contèxt de la logica, son discutits coma proposicions amb variablas que pòdon èsser vertadièras o fausas. Se nomena coma "quantificators" d'elements coma "tot", "algun" o "existís", que semblan indicar la quantitat dins una proposicion logica. Es tanben discutida la construccion de l'afirmacion de predicats amb operators logics coma la conjuncion, disjuncion, e implicacion. D'exemples practics sus cossí provesir los predicats son dessenhats per ajudar los estudiants a comprene quin biais establir la vertat dins las matemàticas discretes.

収穫

  • 📚 Introduction a la logica de predicats dins las matemàticas discretes.
  • 🤔 Explicacion del concèpte de predicat, amb exemples.
  • 🔍 Lo ròtle de quantificadors universals e existencials.
  • 📝 Coma verificar la vertat de predicats amb exemples.
  • 🔗 Utilizacion dels opératores logics: conjuncion, disjuncion, implicacion.
  • 📈 Analisi de l'impacte dels quantificadors dins las proposicions logicas.
  • 🧩 Compausicion de proposicions de predicats utilizant de quantificadors.
  • 🛠 Espleits per medir la vertat dins de proposicions.
  • 🔄 Conversion de proposicions en formulas de predicats logics.
  • 📖 Illustracion dels predicats dins lo domeni de las matemàticas discretes.

タイムライン

  • 00:00:00 - 00:05:00

    Iniziammo il video con delle scuse per la mancata pubblicazione di video recenti a causa di problemi tecnici, promettendo che ci saranno nuovi video in preparazione per aiutare con la matematica discreta, in particolare la logica e le prove. L'argomento del giorno è i predicati, che sono parte della logica dei predicati. Il predicato è fondamentalmente una funzione logica che può essere vera o falsa a seconda del valore variabile, come dimostrato con l'esempio di x maggiore di 3.

  • 00:05:00 - 00:10:00

    Forniti esempi su come distinguere tra soggetto e predicato in una dichiarazione. Usando la logica dei predicati, possiamo determinare la verità o la falsità di un'affermazione sostituendo variabili specifiche come x. Viene data un'ulteriore spiegazione riguardo alle affermazioni composte, che combinano due o più affermazioni usando connettivi come e (congiunzione), o (disgiunzione), implicazione e bi-implicazione, e viene spiegato come esprimere questi concetti usando la logica dei predicati.

  • 00:10:00 - 00:17:44

    Si introduce il concetto di quantificatori nella logica dei predicati, essenziali per esprimere sei o tutte le variabili in una dichiarazione. I principali quantificatori discussi sono il quantificatore universale ('per tutti') e il quantificatore esistenziale ('esiste'). Esempi mostrano come questi quantificatori si applicano alle dichiarazioni matematiche, indicando il contesto in cui una dichiarazione può essere considerata vera.

マインドマップ

Mind Map

よくある質問

  • Que es un predicat dins la logica matematica?

    Un predicat es una proposicion que conten de variables e es valsetuda coma verai o false, segon los valors d'aquestas variables.

  • Coma definisses un predicat amb un exemple simple?

    Un exemple es "x es mai grand que 3", ont "x" es la variabla e "es mai grand que 3" es lo predicat.

  • Quins son los dos tipes principals de logica dins les matemàtiques discretes?

    I a la logica proposicional e la logica de predicats.

  • Que significa un quantificador universal?

    Un quantificador universal, simbolizat per ∀, indica que l'afirmacion es vertadièra per totes los elements d'un domeni.

  • Que significa un quantificador existencial?

    Un quantificador existencial, simbolizat per ∃, indica que i a almens un element dins lo domeni pel qual l'afirmacion es vertadièra.

  • Coma pòt on determinar la vertat d'un predicat utilizant de quantificators?

    La vertat se determina en assignar los valors a las variablas dins lo predicat e verificar se lo resultat complís amb la condicion del quantificador aplicat.

  • Quins exemples de quantificadors existencials se donan en lo video?

    Un exemple es "I a almens un nom per lo qual x = y + 3" qu'es un quantificador existencial verificat coma faus.

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  • 00:00:01
    hi all of you welcome back to ramadin
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    maths academy
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    okay sorry for all uh because uh
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    e4 friday's new videos posted
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    because of the wi-fi and uh some another
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    problems
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    okay and don't need to worry about
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    madame videos a proposed just arrow
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    exams
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    okay don't worry i'm here to help you
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    but
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    logic and proofs means discrete
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    mathematics
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    first chapter logical equivalence truth
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    tables
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    five videos chess you know this is the
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    sixth lecture
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    in our discrete mathematics logic and
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    proofs
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    today's topic is predicates first of all
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    what is the predicate
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    actually in logical groups we have two
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    types of logics is there one
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    is the logically a propositional logic
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    and another one is the
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    predicate logic okay here today we are
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    going to discuss the predicate it's very
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    simple no need to worry
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    you probably couldn't find videos of a
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    question
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    and predicates too and uh remaining
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    videos
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    but be careful this is a very most
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    important topic
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    in your first chapter in discrete
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    mathematics okay now
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    uh you put a predicate i said what is
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    the predicate predicate and then we
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    suppose i'll consider one statement
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    listen carefully it's very important
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    suppose x
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    is greater than 3 beta x is greater than
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    3 then what is the predicate and how
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    we are defined this suppose in terms of
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    how we can
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    write x greater than 3 x is
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    greater than
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    3 x is a
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    variable
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    one is the variable another one is the
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    logic that is see this x is the
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    variable now that is called the subject
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    that is called the subject of the
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    statement
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    and greater than three e greater than
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    three
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    months that is the predicate of the
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    statement the nuance
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    logic is it clear x is greater than
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    three
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    here x is the subject and three is
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    greater than
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    three this is our predicate
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    okay statement even right
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    now p of x
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    is nothing but the predicate p is what
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    better
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    predicate okay x is what
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    that is a variable okay
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    x is what the variable we can define the
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    statement
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    like this also now i'll give uh some
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    examples of
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    predicates
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    [Music]
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    sometimes either it may be true or it
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    may be
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    false depends upon the statement okay
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    let p of x denotes the statement x is
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    greater than three
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    and a germany gamma naturally x is
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    greater than three
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    okay what are the truth values of
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    p r four and p of two and to narrow
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    actually first of all what is the
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    predicate of the statement we already
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    discussed what is the predicate here
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    then predicate any more to the beta x
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    greater than three k
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    p of x is the predicate here p is the
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    predicate and x is a
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    variable okay our predicate is greater
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    than three
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    if you consider in the place of p and
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    event nano this is what this is what is
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    a given statement
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    here how we can write the predicate
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    is what x greater than three the
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    predicate
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    is what the predicate
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    is x greater than three and they can
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    even each have to
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    find out p half 4 we can write
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    x greater than 3 in terms of the
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    predicate we can write p
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    of x okay if you consider p
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    of 4 means in the place of x what we
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    have to do
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    substitute 4 then it will become 2 if
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    you consider
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    p of 4 if p of 4
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    and 20 then x is equal to
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    4 x is equal to 4 this
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    4 is greater than 3 means what
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    p of 4 is a true this this is having
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    truth value okay or else you can write
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    it is
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    false therefore therefore
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    p of 4 is
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    true what is the truth value of this p
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    of 4 is true then check it p of 2
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    okay we have 2 we have to ante
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    explicitly in this call new to this
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    quality what is our statement x is
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    greater than three
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    if you consider two is greater than
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    three
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    a one two nano x is e or else you can
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    write x is equal to 2
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    in the predicate logic then 2 is greater
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    than
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    3 this is what which is wrong statement
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    2 is greater than 3 no therefore when we
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    even write
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    minimum therefore p of 2
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    is false is not
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    false like that you can verify whether
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    the statement is true
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    or false by using predicate logic and
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    one more example an important one is
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    qr fix denotes the statement x is equal
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    to y
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    plus 3 this is x is equal to y plus 3
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    listen carefully what are the truth
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    values of
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    proposition q of 1 comma two q
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    of three comma zero first of all the
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    given
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    logic you can write in terms of
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    predicate
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    eighth german key x is equal to y plus
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    three we need
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    to predict
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    what is the given statement here ah
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    they already defined in terms of q along
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    the x and y log the and then the
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    the function the predicate logic it
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    defines in terms
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    of it could be of x law denote this
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    requirement
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    narrow q of x comma y here x and y
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    are the variables what is the condition
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    the condition is x is equal to y plus 3
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    that is the predicate
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    in that case what we have to do now i
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    will going to consider this
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    here my logic intended what is the given
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    one here
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    x is equal to y plus 3 here
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    what is our x value x is equal to 1
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    and y is equal to 2 put here what will
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    happen
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    this is 2 plus 3 this is what 1
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    is equal to 5 no it is a false
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    then you can write it as it is a false
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    therefore
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    therefore q of 1 comma
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    2 the predicate is false like that
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    you can write the truth values of the
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    predicates now consider
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    this here x is equal to what 3 y is
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    equal to what
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    0 then how we are going to write what is
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    the statement y is equal to x is equal
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    to y plus 3
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    3 is equal to what beta here y is 0 3
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    both are same and the empty the
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    statement predicate logic sometimes
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    either it may be true
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    or it may be false okay
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    therefore in dq
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    zero is true in the
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    predicate logic is it clear just note
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    okay it
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    statement in predicate logic in that
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    compound statement means
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    we have two or more statements or
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    minimum two statements is there
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    by using our connectives what is our
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    connectives
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    conjunction disjunction and
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    implication by implication by using
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    these four you have to write the
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    combination of those
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    statements that is the compound
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    statement of the
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    predicates statements
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    a teacher her teaching is good this is
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    one statement and this is another
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    statement here what we have to do
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    in ehm understand the first statement
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    rama is a teacher
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    and her teaching is good
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    i'm contented antibodies over
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    here what is our connective conjunction
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    what is that anthony indicate then
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    condom on the first of all you have to
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    identify
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    which is the subject and which is the
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    predicate in the given statement
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    [Music]
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    that is what our subject rama is a
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    subject then what is ramay's
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    teacher teacher means it indicates the
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    logic that is what it it is what
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    predicate predicate
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    and in even write you or we can
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    write it as predicate logic
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    and then the predicate teacher predicate
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    me teacher
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    okay and
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    her teaching is good and here
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    teaching is the subject
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    teaching is the subject good
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    is the predicate okay then how we are
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    going to write predicate logic is what
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    it stands
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    good then what is the variable here
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    teaching means you can write t
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    like this
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    okay this is what the
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    compound statement how we are going to
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    write the compound statement by using
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    the connective also
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    kind or then or
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    if and only
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    we already know that how we are going to
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    write the predicate rama is a teacher
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    rama is the variable subject and t is
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    the
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    teacher predicate or r means
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    like this her teaching is good means or
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    teaching
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    is the subject good is the predicate
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    means what
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    g of t then even i cho t of
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    r then then and entry
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    like this implies
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    g of t okay like that we can write the
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    compound statements of the predicates
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    next we will discuss the
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    quantifiers okay
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    see all of you next and most important
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    one is the quantifier quantifier
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    statement quantifier and the intent
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    suppose just just observe these four
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    statements
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    okay or prepositions
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    anything all students have books
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    okay all students having books that is
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    one statement
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    and some moments are tall or short
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    now whatever it may be but here hall and
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    some it could have
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    no one sit in the class no one
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    for every integer x x square
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    is non-negative integer in these
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    four statements in this four statement
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    all some know one for every each and
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    every
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    statement indicates by using these four
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    values
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    these four terms those terms are called
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    it as
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    quantifiers you know in this statement
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    all sum no one there exist or for every
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    like that that is associated with some
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    quantity or with some statement those
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    statements are called it as what
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    quantifiers in the quantifiers we have
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    two types one is the universal
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    quantifier
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    then another one is the existential
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    quantifier now we will discuss what is
  • 00:13:25
    universal quantifier
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    and what is the existential quantifier
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    law
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    see all of you here universal quantifier
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    universal quantifier
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    but for all all values and this
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    kundalini call it that is universal
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    i want to know the universal quantifier
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    of p of x is the statement what is the
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    statement here
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    p of x for all values of x
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    and the universal law for all values and
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    you mentioned just arrow
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    in the domain d for example
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    [Music]
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    is the universal quantifier of the
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    predicate
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    p of x and here for all
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    is called what universal quantifier
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    this is the universal quantifier
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    here we read it as for all p x
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    or else for every x p x and j
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    for example i'll consider one small
  • 00:14:36
    statement p of x this
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    statement x plus 1 greater than x
  • 00:14:40
    what is the truth values of the
  • 00:14:43
    quantifier
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    for all x p of x where the domain
  • 00:14:47
    consists
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    for all the real numbers and into the
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    the given statement of the predicator p
  • 00:14:55
    of x
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    is what x plus 1 is greater than
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    x okay that is the given statement
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    then how we are going to write the
  • 00:15:05
    quantifier
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    p of x is true why because for all
  • 00:15:09
    values of the real numbers
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    you know the statement which
  • 00:15:17
    when it is true uh of the quantifier
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    all the real values and payment render
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    this is the statement
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    if you consider the quantifier of the
  • 00:15:29
    statement in terms of
  • 00:15:30
    pr x it is true
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    for all true for all
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    the real numbers x is for all
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    real numbers the quantifier
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    for all x p x is true okay
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    like that you can write the universal
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    quantifiers now
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    next we'll discuss the existential
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    quantifiers okay now down
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    see existential quantifier and indent
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    then there exist at least one element in
  • 00:16:06
    the
  • 00:16:06
    given statement for example i will
  • 00:16:08
    consider qr fix
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    denotes the statement what is our
  • 00:16:12
    statement x is equal to
  • 00:16:14
    x plus 3 and here what
  • 00:16:17
    is the truth values of the
  • 00:16:19
    quantification
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    of there exist x belongs to q of x
  • 00:16:24
    where the domain consists for all real
  • 00:16:28
    numbers
  • 00:16:29
    what is our given statement first you
  • 00:16:31
    have to write the
  • 00:16:32
    given statement consider it as p q of x
  • 00:16:36
    for your wish p of x
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    okay that is one statement x is equal to
  • 00:16:41
    x plus 3 then q of x is true
  • 00:16:45
    when it is for all real numbers
  • 00:16:48
    okay if you take for all real numbers
  • 00:16:52
    the statement is true if you take one
  • 00:16:54
    then it will what will happen one is
  • 00:16:56
    equal to what
  • 00:16:57
    one is equal to had one plus three and
  • 00:17:00
    demo
  • 00:17:01
    one is equal to four both are equal no
  • 00:17:03
    for all real numbers it is not
  • 00:17:06
    true and the rexist x
  • 00:17:09
    q of x is false means this is not
  • 00:17:13
    existence okay this is the existential
  • 00:17:16
    quantifier
  • 00:17:19
    [Music]
  • 00:17:39
    thanks for watching
タグ
  • Predicat
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