Predicate truth set definition

Definition: The truth set of a predicate is the collection of all elements in its domain where the predicate evaluates to \(T\).

Notice that specifying the domain and the truth set is sufficient for defining a predicate.

Predicate truth set example

The truth set for the predicate \(V(x)\) is \(\underline{\phantom{\{ x ~\mid~ V(x) = T\} = \{ 001, 010, 011 \}}}\).

The truth set for the predicate \(N(x)\) is \(\underline{\phantom{\{ x ~\mid~ N(x) = T\} = \{ 101, 111 \}}}\).

The truth set for the predicate \(Mystery(x)\) is \(\underline{\phantom{\{ x ~\mid~ Mystery(x) = T\} = \{ 000, 001, 010, 101, 111 \}}}\).