Give an example of relation $R$ and $S$ on $A$ such that $R$ and $S$ are nonempty, and $R \circ S$ and $S \circ R$ are empty Let $A = \left \{a, b, c, d\right \}$, give an example of relation $R$ and $S$ on $A$ such that $R$ and $S$ are nonempty, and $R \circ S$ and $S \circ R$ are empty
I'm thinking of ways that a set could be empty, and the only thing I can think of is that if two sets are disjoint, then their intersection is empty. However, I'm not sure as to how to go about coming up with the relations. Could someone give me a hint.

How about the simplest relations you can think of: $R=\{(a,a)\}$ and $S=\{(b,b)\}$
Why are $R\circ S$ and $S\circ R$ empty. Try to generalize.
