Assume the School database shown in the Appendix. Write the following queries in $(1)$ relational algebra and $(2)$ SQL$.$ State your as sumptions 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$($nnajor$\_$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. $(1$:$2$points$)$