CODEWITHSUNDEEP
relational-algebra
Kevin Spaghetti
Kevin Spaghetti

Reputation: 758

Finding proper subset of elements using relational algebra

I have one table called Exams composed by the columns student and exam and i need to find all the students that took a proper subset of the Exams taken by the student A.

A sample of data could be:

student exam
A       1
A       2
B       1
B       3
C       1
C       2
D       1

And the result should be

student
D

Because only D took a proper subset of the exams taken by A, B is not in the result because he took an exam that A has not taken

What i came up with so far is:

take all the exams that the student A has taken 

examsA ← π exam (σ student='A' (Exams))

divide the Exams relation by the exams the student A as taken 

studentsNoGood ← Exams ÷ examsA

now i have all the students that took exactly the same exams and those who took more exams, by substracting i find only those who took less exams and those who did not take a subset of the student 'A' exams.

lessExamsOrNotSubset ← Exams - studentNoGood

And then im stuck on how to differentiate those with less exams and those who took unrelated exams


With 'a proper subset' i mean that with 2 sets D and E, D is a proper subset of E iff D is contained in E and D is not equal to E, so there is an element of E that is not in D.

I am using the relational algebra found in the book Fundamentals of Database Systems (Elmasri, Navathe). page 239

Upvotes: 1

Views: 454

Answers (1)

Renzo
Renzo

Reputation: 27424

To find the students that took exams unrelated to those of A first find those exams:

R1 ← π exam (Exams) - examsA

then find the students with at least one exam in this set:

studentsUnrelated ← π student (Exams ⨝(Exams.exam = R1.exam) R1)

Then you can remove also these students to find those that have taken only a proper subset of the exams of A.

Upvotes: 1

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