Let R and S be transitive binary relations on the same set A$.$ Which of the following new relations must also be transitive?

Hint: For each part, justify your answer with a brief argument if the new relation is transitive or with a counter example if it is not.

$($a$)$ R$-1($b$)$ R $\backslash$cap S $($c$)$ R o R $($d$)$ R o S