Definition:Propositional Function/Examples

Examples
Let the universe be the set of integers $\Z$.

Let $P \left({x}\right)$ be the propositional function defined as:
 * $x$ is even

Then we can insert particular values of $x \in \Z$, for example, as follows:

Thus $P \left({x}\right)$ is a unary propositional function (pronounced yoo-nary).

Let $P \left({x, y}\right)$ be the propositional function defined as:
 * $x$ is less than $y$

Then we can create the propositional statements:

Thus $P \left({x, y}\right)$ is a binary propositional function.

Let $P \left({x, y, z}\right)$ be the propositional function defined as:
 * $x$ is between $y$ and $z$.

Then:

Thus $P \left({x, y, z}\right)$ is a ternary propositional function.