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.

Exercise 2 (Lossless Decomposition, Dependency Preservation)

Suppose we do not have access to the full data set of flights, but we are able to sample 250 flights at random from the table. We would like to estimate the percentage of flights that are delayed.  To do this, we sum the number of flights in our sample and divide by 250 (and multiply by 100).  We then resample with replacement from our sample many times, each time computing this statistic (sum of delayed flights / 250 * 100).  With this process, we obtain a 95% confidence interval: (23.7%, 64.3%).  Choose all the correct statements:

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.

Consider the relation schema R(A, B, C, D, E) and the set F = {B → D, CD → E, E → A, A → BC} of functional dependencies. Assume that R is decomposed into the relation schemas R1(A, B, C, E) and R2(B, D). Use the Nonadditive Join Test for Binary Decomposition to determine if this is a lossless decomposition. Further, test and explain whether it is dependency preserving.