$2.$ Assume the School database shown in the Appendix. Write the following queries in $(1)$ relational algebra and $(2)$ SQL$.$ State your assumptions if the semantics are not clear.

STUDENTS$($student$\_$id$,$ first$\_$name, last$\_$name, email, major$\_$code, class$\_$year$)$

COURSES$($course$\_$id$,$ course$\_$name, course$\_$description, credits, department$\_$code$)$

ENROLLMENTS$($student$\_$id$,$ course$\_$id$,$ semester, grade$)$

MAJORS$($major$\_$code, major$\_$name, department$\_$code$)$

DEPARTMENTS$($department$\_$code, department$\_$name$)$

$($a$)$ Count the number of students in each department. $(12$ points$)$

b$)$Find the course names and the number of students who have taken each course, sorted by the number of students in descending order. $(12$ points

c$)$Find the courses with the highest average grades. $(12$points$)$