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

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

Summary

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.

Takeaways

  • 📚 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.

Timeline

  • 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.

Mind Map

Mind Map

Frequently Asked Question

  • 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]
  • 00:14:13
    is the universal quantifier of the
  • 00:14:15
    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
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    what is the truth values of the
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    quantifier
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    for all x p of x where the domain
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    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
  • 00:16:03
    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
  • 00:16:10
    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
  • 00:16:21
    of there exist x belongs to q of x
  • 00:16:24
    where the domain consists for all real
  • 00:16:28
    numbers
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    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
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    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
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    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
Tags
  • Predicat
  • Quantificador
  • Logica
  • Matematicas discretes
  • Taulas de vertat
  • Logica proposicionala
  • Quantificadors universals
  • Quantificadors existencials
  • Conjuncion
  • Disjuncion
  • Implicacion