>[!summary] A predicate is a type of proposition without a definite fixed truth value >[!info]+ Read Time ⏱ **1 min** # Definition A predicate is a type of [[Propositions|propositions]] without a definite fixed value. Its value is instead dependent on one or more variables[^1] ## Examples A simple example of this logic is $\text{x is greater than 5}$ Our predicate $P(x)$ is true or false depending in the value of x we choose. $\begin{align} P(x) : x > 5 \\ P(7) : 7 > 5 \\ P(3) : 3 > 5 \end{align}$ When we have values of $P(7)$ the statement is true, but with a value of P(3) the statement is false --- A physical example could be something such as: Let $T(x):$ "x is a triangle" $\begin{array}{c} T(\text{Pizza slice} ) : \text{true}\\ T(\text{circle}) : \text{false} \end{array}$ The truth value of $T(x)$ is dependent on the value of x. --- 📂 Want to see more structured notes like these? Help grow the project by [starring Math & Matter on GitHub](https://github.com/rajeevphysics/Obsidan-MathMatter). --- [^1]: Definition adapted from Dr. Robert Talbert