Let $\displaystyle R$ be a transitive relation defined on a set $\displaystyle B$. Prove or disprove that $\displaystyle R^4$ is a transitive relation.

I'm inclined to believe that it's true, but I can't be sure. I at least know this: A relation $\displaystyle R$ is transitive on a set $\displaystyle A$ if whenever $\displaystyle (a,b)\in R$ and $\displaystyle (b,c)\in R$, then $\displaystyle (a,c)\in R$, $\displaystyle \forall a,b,c\in R$