1. ## 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 n²>n)
b) True. Negation is, "When x<0 there is y such that y^2=x
c) No clue :P

2. ## Re: Predicates and Negation

Originally Posted by Plonker

a) Predicate. Negation is ¬(∃n ∈ N n²>n)
b) True. Negation is, "When x<0 there is y such that y^2=x
c) No clue :P
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.