Find the names of students who are not enrolled in any course - Students, Faculty, Courses, Offerings, Enrolled - relational-algebra

Question

Given the database below, project the names of the students who are not enrolled in a course using relational algebra.
Students(snum, sname, major, standing, age, gpa)
Faculty(fid, fname, deptid)
Courses(cnum, cname, course_level, credits)
Offerings(onum, cnum, day, starttime, endtime, room, max_occupancy, fid)
Enrolled(snum, onum)
I can get the snum of all students not enrolled in a course with:
π snum Students - π snum Enrolled
But how do I project the sname of the student with the snums that I find?

Answer 1

Every base table holds the rows that make a true proposition (statement) from some (characteristic) predicate (statement template parameterized by columns). The designer gives the predicates. The users keep the tables updated.
-- rows where student [snum] is named [sname] and has major [major] and ...
Students
-- rows where student [snum] is enrolled in offering [onum]
Enrolled
Every query result holds the rows that make a true proposition from some predicate. The predicate of a relation expression is combined from the predicates of its argument expressions depending on its predicate nonterminal. The DBMS evaluates the result.
/* rows where
student [snum] is named [sname] and has major [major] and ...
AND student [snum] is enrolled in offering [onum]
*/
Student ⨝ Enrolled
AND gives NATURAL JOIN, ANDcondition gives RESTRICTcondition, EXISTScolumns gives PROJECTother columns. OR & AND NOT with the same columns on both sides give OR & MINUS. Etc.
/* rows where
THERE EXISTS sname, major, standing, age & gpa SUCH THAT
student [snum] is named [sname] and has major [major] and ...
*/
π snum Students
/* rows where
THERE EXISTS onum SUCH THAT
student [snum] is enrolled in offering [onum]
*/
π snum Enrolled
/* rows where
( THERE EXISTS sname, major, standing, age & gpa SUCH THAT
student [snum] is named [sname] and has major [major] and ...
AND NOT
THERE EXISTS onum SUCH THAT
student [snum] is enrolled in offering [onum]
)
AND student [snum] is named [sname] and has major [major] and ...
*/
(π snum Students - π snum Enrolled) ⨝ Students
You can project out any columns that you don't want from that.
(Notice that we don't need to know constraints to query.)
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