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: Prove that regular languages are closed under intersection and set difference. (05 marks) Must prove using DeMorgan’s Law. Solution:
Typology: Assignments
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Enrollment ( StudentID , courseID , course_Instructor , Student_Name , Student_Degree , Student_ADD , course_Name , Instructor_Name , Instructor_Office , Grade) StudentSupervisor ( StudentID* , specialization , supervisor)
Enrollment relation is not in the first Normal Form because the Attribute Student_Degree is not Atomic. So we decompose as following: Enrollment (StudentID , courseID , course_Instructor , course_Name Student_Name , Student_ADD, Instructor_Name , Instructor_Office , Grade) Student_Degree (StudentID* , courseID, StudentDegree) -- The resulted relations will be: Enrollment (StudentID , courseID , course_Instructor , course_Name Student_Name , Student_ADD, Instructor_Name , Instructor_Office , Grade) Student_Degree (StudentID , courseID, StudentDegree) StudentSupervisor (StudentID , specialization , supervisor)
- Second Normal Form: 1- First we state the FDs for the Enrollment relation StudentID , courseID , Grade √ StudentID Student_Name , Student_ADD. X courseID course_Name , course_Instructor , Instructor_Name , Instructor_Office , X -------------- Enrollment relation is not in the second normal form because only grade attribute is fully functionally dependent on the primary key. However, Student_Degree and StudentSupervisor relations are both in the second normal form. 2- second we decompose: Course_grade (StudentID , CourseID , Grade ) Student (StudentID , Student_Name , Student_ADD ) course (courseID , course_Name , course_Instructor , Instructor_Name , Instructor_Office ) the resulted relations will be : Course_grade (StudentID , CourseID , Grade ) Student (StudentID , Student_Name , Student_ADD ) course (courseID , course_Name , course_Instructor , Instructor_Name , Instructor_Office ,.) StudentSupervisor (StudentID* , specialization , supervisor) Student_Degree (StudentID* , courseID*, Student_Degree)