1. Functional Dependencies Quiz

2. Project Relation Attributes project name – pname start date – start budget customer name – cname customer phone – cphone customer email – cemail employee SIN – sin employee first name – fname employee last name – lname employee category - cat (employee's occupation, e.g. welder, electrician) employee rating – rank (a measure of seniority, a senior electrician might have a rank of 3) employee hourly rate – rate (charged to customers) machine ID – mid machine description – desc machine model – model machine weight – weight machine size – size machine cost – cost hours worked on a project by an employee - hours

3. Functional Dependencies pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget (one start date and budget) cname  cphone, cemail (a customer has one phone and email) pname  cname (projects are for only one customer) sin, pname  hours (number of hours an employee works on a project) sin  fname, lname (a customer has one first and one last name) sin, fname, lname  cat, rank, rate (an employee has a categoty, rank and rate) cat, rank  rate (the rate is derived from category and rank) mid  desc (each machine has a description) mid  model, cost (a machine is of a model, and has a cost) mid, model  weight, size (a machine of a model type has a weight and size) model  weight, size (weight and size are the same for machines of a model) mid  pname (machines are only assigned to one project)

4. Armstrong's Axioms pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is mid  weight implied by F? Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z

5. Armstrong's Axioms pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is mid  sin implied by F? Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z

6. Armstrong's Axioms pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is sin, mid  fname, lname implied by F? Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z

7. Armstrong's Axioms pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is sin, mid  hours implied by F? Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z Reflexivity – if X  Y, then X  Y Augmentation – if X  Y, then XZ  YZ Transitivity – if X  Y, and Y  Z then X  Z Union – if X  Y and X  Z, then X  XZ Decomposition – if X  YZ, then X  Y and X  Z Pseudotransitivity – if X  Y and WY  Z, then XW  Z

8. Attribute Closure pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Compute the attribute closure of {sin, mid} Is {sin, mid} a superkey? Compute the canonical cover of F

9. BCNF and Third Normal Form pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is machine = {mid, model, cost, weight, size} in BCNF? 3NF?

10. BCNF and Third Normal Form pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is company = {cname, cphone, cemail} in BCNF? 3NF?

11. FBCNF and Third Normal Form pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is works = {sin, pname, mid, hours} in BCNF? 3NF?

12. Database Characteristics pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Consider the set of relation schema: machine = {mid, cost, mid, hours}, model = {model, cost, weight} Do the schemas form a lossless join? Are they dependency preserving? Consider the set of relation schema: machine = {mid, cost, mid, hours}, model = {model, cost, weight} Do the schemas form a lossless join? Are they dependency preserving?

13. Database Characteristics pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Consider the set of relation schema: works = {sin, mid, hours}, machine_use = {mid, pname} Do the schemas form a lossless join? Are they dependency preserving? Consider the set of relation schema: works = {sin, mid, hours}, machine_use = {mid, pname} Do the schemas form a lossless join? Are they dependency preserving?

14. Decomposition pname start budget cname cphone cemail sin fname lname cat rank rate mid desc model weight size cost hours pname, cname  start, budget cname  cphone, cemail pname  cname sin, pname  hours sin  fname, lname sin, fname, lname  cat, rank, rate cat, rank  rate mid  desc mid  model, cost mid, model  weight, size model  weight, size mid  pname Is the project relation in 1NF or 2NF? Produce a 3NF, dependency preserving decomposition of the project relation