Consider the ER schema for the MOVIES database as below. In the ER schema, ACTOR is used as a generic term and includes actresses. Given the constraints shown in the ER schema, answer the following statements with true or false. Explain why.

$($a$)$ There are some actors who have not performed in any movie.

$($b$)$ A movie can have no lead actor.

$($c$)$ Every director has been an actor in some movie.

$($d$)$ An actor can be a director and producer at the same time.

$($e$)$ Every producer has been an actor.

$($f$)$ A movie has one director, but many producers.

$($g$)$ Every movie has a director who also acted in that movie.

$($h$)$ A producer cannot be an actor in some other movie.

$($i$)$ Every producer should produce one or more movies.

$($j$)$ A movie can have two lead actors.