# Definition:Propositional Function/Examples

## Examples

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

Let $\map P x$ be the propositional function defined as:

$x$ is even

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

 $\displaystyle \map P 1$ $=$ $\displaystyle \F$ $\displaystyle \map P 2$ $=$ $\displaystyle \T$ $\displaystyle \map P {591}$ $=$ $\displaystyle \F$

Thus $\map P x$ is a unary propositional function (pronounced yoo-nary).

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Let $\map P {x, y}$ be the propositional function defined as:

$x$ is less than $y$

Then we can create the propositional statements:

 $\displaystyle \map P {1, 2}$ $=$ $\displaystyle \T$ $\displaystyle \map P {2, 1}$ $=$ $\displaystyle \F$ $\displaystyle \map P {3, 3}$ $=$ $\displaystyle \F$

Thus $\map P {x, y}$ is a binary propositional function .

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Let $\map P {x, y, z}$ be the propositional function defined as:

$x$ is between $y$ and $z$.

Then:

 $\displaystyle \map P {1, 2, 3}$ $=$ $\displaystyle \F$ $\displaystyle \map P {2, 1, 3}$ $=$ $\displaystyle \T$ $\displaystyle \map P {5, 4, 3}$ $=$ $\displaystyle \F$

Thus $\map P {x, y, z}$ is a ternary propositional function .

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