Another type of rule, type $($I$),$ is those of the form B $->$ Ac$.$

$($a$)$ My friend Reggie got types $($II$),($III$),$ and $($IV$)$ correct, but used type $($I$)$ instead of type $($I$).$ Reggie insists that it is ok$,$ because he still gets exactly the regular languages. Is he correct? Explain carefully.

$($b$)$ My friend Fred uses rules of types $($I$),($II$),($III$),$ and $($IV$)$ as well as rules of type $($I$).$Fred insists that it is ok$,$ because he still gets exactly the regular languages. Is he correct? Explain carefully.