Let A be a set with $\lvert A \rvert$ = $4$. What is the max number of elements tht a relation R on A can contain so tht $R \cap R^{-1}$ = $\emptyset$

Question

Let A be a set with $\lvert A \rvert$ = $4$. What is the maximum number of elements that a relation R on A can contain so that $R \cap R^{-1}$ = $\emptyset$?

I am not sure at all how to start this and my instructor says that it does not require a formal proof.