# Language and Finite Models

Let us consider the language consisting of one symbol $R$ for a binary relation. Let $\sigma$ denote the following sentence:

$\forall x \exists y \exists z \ x\neq y \wedge y \neq z \wedge x \neq z \wedge x R y \wedge z R x$.

Does $\sigma$ have a finite model? I know that if $S$ is an interpretation structure for a set of formulas $\Gamma$, $S$ is called a model for $\Gamma$, written $S \models \Gamma$, if all the formulas in $\Gamma$ are true in $S$. How would I show this? Thanks

HINT: Think of a triangle whose vertices represent the points of the model, and whose edges represent the relation $R$.