Logical Predicate

Definition

A predicate is a sentence that contains a finite number of variables and becomes a statement when specific values are substituted for the variables Predicates can be obtained by removing some or all nouns from a statement

Example

let P stand for “is a student at NUS” let Q stand for “is a student at” P and Q are predicate symbols

$P(x)=$ ”$x$ is a student at NUS” $Q(x,y)=$ ”$x$ is a student at $y$” $x$ and $y$ are predicate variables

Domain

The domain of a predicate variable is the set of all values that may be substituted in place of the variable

Truth Set

If $P(x)$ is a predicate and $x$ has domain $D$, the truth set is the set of all elements of $D$ that make $P(x)$ true when they are substituted for $X$ Denoted as $\{x\in D|P(x)\}$