I have three relations:
Course(courseNum, units, time, room)
Student(ID, name, degree)
Takes(ID, courseNum)
I need a relational algebra expression that shows a list of courses that have no graduate student plus associated information (courseNum, units, time, room).
How can I use the relational algebra to find a relation that indicates "this course does not have grad students"?
how can I use the relational algebra to find a relation that indicates this course does not have grad students?
R MINUS S holds rows that are in R but not in S.
So if R with attributes r1, ... holds tuples that make a true proposition (statement) from some (characteristic) predicate (sentence template) r parameterized by r1, ... and S with attributes r1, ... holds tuples that make a true proposition from some predicate s in terms of r1, ... then R MINUS S holds tuples that make a true proposition from predicate rAND NOTs.
Similarly JOIN corresponds to AND, UNION to OR, PROJECTattributes kept to EXISTSattributes dropped, RESTRICTcondition to ANDcondition, etc. That is how we know how to build a particular query--we use relation operators that return the tuples we want given that the base/named relations hold (via updates) the tuples satisfying their predicates (per the design).
(To use MINUS & UNION we sometimes have to rearrange a predicate expression to get argument expressions with the same attributes. And we have get any NOTs to appear in AND NOT. Often this is done by applying De Morgan's laws & distributive laws. Find the names of students who are not enrolled in any course - Students, Faculty, Courses, Offerings, Enrolled)
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