- Predicate (logic)
Sometimes it is inconvenient or impossible to describe a set by listing all of its elements. Another useful way to define a set is by specifying a property that the elements of the set have in

**common**. The notation "P(x)" is used to denote a sentence or statement**P**concerning the variable object x. The set defined by "P(x)" written {x | "P(x)"}, is just a collection of all the objects for which**P**is sensible and true.For instance, {x | x is a positive integer less than 4} is the set {1,2,3}.

Thus, an element of {x | "P(x)"} is an object

**t**for which the statement**P(t)**is true. Such a sentence "P(x)" is called a**"Predicate**". "P(x)" is also called a**"propositional function**", because each choice of x produces a proposition "P(x)" that is either true or false.In formal

semantics a**predicate**is an expression of the semantic type ofset s. An equivalent formulation is that they are thought of asindicator function s of sets, i.e. functions from anentity to atruth value .In

first-order logic , a predicate can take the role as either a property or a relation between entities.**ee also***

Set-builder notation makes use of predicates

*Free variables and bound variables **External links*** [

*http://cs.odu.edu/~toida/nerzic/content/logic/pred_logic/predicate/pred_intro.html Introduction to predicates*]

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