Exercise 1 (Armstrong Axioms, Functional Dependencies) [30 points]

Given database schema: Faculty (fid, name, tenured, dname, salary, chairID)Department (dname, phoneNumber, numberOfFaculty)Course (fid, dname, semester, cname) Write an assertion check in SQL for the following condition: The salary of any faculty member cannot be greater than their chair’s salary.

Consider the relation schema R(A, B, C, D, E) and the set F = {AB → C, CD → E, DE → B} of functional dependencies. Find all candidate keys of R by using the tableau (7‐step) method. Explain the steps.

We decide to save time by sampling 1000 flights at random from a single month (instead of 250 from the whole data set) and then using the same process to get a confidence interval for the percentage of flights in the year that are delayed. Is this a good idea? Choose all the correct statements.

Given database schema: Faculty (fid, name, tenured, dname, salary, chairID)Department (dname, phoneNumber, numberOfFaculty)Course (fid, dname, semester, cname) Write an assertion check in SQL for the following condition: The salary of any faculty member cannot be greater than their chair’s salary.

Consider the following relation r with the schema R(A, B, C). Find all non-trivial functional dependencies that can be derived from the data in r. Give reasons for your answer. A B C b c h e i f g i f e b a

Consider the relation schema R(A, B, C, D, E) and the set F = {A → B, B → CE, D → AE} of functional dependencies. Show that the FD AB → AC is logically implied by F by using Armstrong’s axioms only (do not use the derived inference rules and the attribute closure algorithm).

Consider the relation schema R(A, B, C, D, E) and the set F = {AB → C, CD → E, DE → B} of functional dependencies. Find all candidate keys of R by using the tableau (7‐step) method. Explain the steps.

Livor mortis is due to the abundant of calcium ions in the sarcoplasm.

Consider the relation schema R(A, B, C, D, E, F) and the set S = {AB → C, BC → AD, D → E, C → B} of functional dependencies. Assuming that R is decomposed into the relation schemas R1(A, B), R2(B, C), R3(A, B, D, E), and R4(E, F). Use the Chase test to show if this is a lossless decomposition.