$1.$ State whether each of the following is true or false. If false, explain why.

$(1)$ Base$-$class constructors are not inherited by derived classes.

$(2)$ An is$-$a relationship is implemented via composition.

$(3)$ A Student class has an is$-$a relationship with the Faculty and Course classes.

$(4)$ Private members of a private base class are inaccessible to the derived class.

$(5)$ A base class$$s protected members can be accessed in the base$-$class definition, in derived$-$class definitions and in friends of the base class and its derived classes.

$2.$

Draw an inheritance hierarchy for students at a university. Use Student as the base class of the hierarchy, then include classes UndergraduateStudent and GraduateStudent that derive from Student. Continue to extend the hierarchy as deep $($i$.$e$.,$ as many levels$)$ as possible. For example, Freshman, Sophomore, Junior and Senior derive from UndergraduateStudent, and DoctoralStudent and MasterStudent derive from GraduateStudent. After drawing the hierarchy, discuss the relationships that exist between the classes. $($Note: You don$$t need to write any code for this exercise.$)$