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Thread: Predicates and Negation

  1. #1
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    Predicates and Negation




    I'm unsure about these three, here are my attempts. Please also explain the difference between a predicate and true/false. I assumed it is a predicate when it can be either true or false.


    a) Predicate. Negation is (∃n ∈ N n>n)
    b) True. Negation is, "When x<0 there is y such that y^2=x
    c) No clue :P


    Your help is truly appreciated!
    Last edited by Plonker; Mar 9th 2017 at 06:31 AM.
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  2. #2
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    Re: Predicates and Negation

    Quote Originally Posted by Plonker View Post


    a) Predicate. Negation is (∃n ∈ N n>n)
    b) True. Negation is, "When x<0 there is y such that y^2=x
    c) No clue :P
    About predicates:
    Predicates are also commonly used to talk about the properties of objects, by defining the set of all objects that have some property in common. So, for example, when P is a predicate on X, one might sometimes say P is a property of X. Similarly, the notation P(x) is used to denote a sentence or statement P concerning the variable object x. The set defined by P(x) is written as {x | P(x)}, and is just a collection of all the objects for which P is true.
    For instance, {x | x is a natural number less than 4} is the set {1,2,3}.
    If t is an element of the set {x | P(x)}, then the statement P(t) is true.
    Here, P(x) is referred to as the predicate, and x the subject of the proposition. Sometimes, P(x) is also called a propositional
    function, as each choice of x produces a proposition.
    A simple form of predicate is a Boolean expression, in which case the inputs to the expression are themselves Boolean values, combined using Boolean operations. Similarly, a Boolean expression with inputs predicates is itself a more complex predicate.

    You are correct on the first two. I don't know enough number theory to quickly solve c).
    You could write the negation of the statement.
    Last edited by Plato; Mar 9th 2017 at 09:31 AM.
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