The complement of a digraph has the same vertex set as the original digraph, and an arc...

The complement of a digraph has the same vertex set as the original digraph, and an arc from x to y exactly when the original digraph does not have an arc from x to y. The two digraphs shown below are complementary. Call a digraph symmetric (transitive) iff its relation is symmetric (transitive).

(a) Show that the complement of a symmetric digraph is symmetric.

(b) Show by example that the complement of a transitive digraph need not be transitive.