Consider the following relation schema for table R:

R(ENo, DNo,PNo,EName, DName,PName,Edob,PCity,PCountry, hours,rate)

Attributes starting with E refer to Employees, those starting with D refer to Departments, and those with P to Projects. Employees, Departments, and Projects are identified by unique numbers. The number of hours and hourly rate of pay for an employee to carry out a project are determined by himself/herself and the project. There may be multiple projects that are conducted in a department and multiple departments can be involved in a single project as well. Any employee can be affiliated with a few different departments and work in multiple projects at the same time. A project may involve multiple employees. Names for employees, departments and projects are not generally unique. A project will only be conducted in a single city. Multiple cities from the same country may appear in the table, however, cities are uniquely named within and across all countries.

Answer the following questions:

(a) Identify the Functional Dependencies in R. Be sure to only include functional dependencies that satisfy the following 4 rules: 1) Only include non-trivial FDs; 2) Minimize the determinant (LHS), that is, only include full FDs; 3) Maximize the RHS; and 4) Only include FDs that cannot be derived from other FDs using Armstrongs axioms. Please refer to Page 26 of the Module 10 lecture notes for the details of the above requirements.

(b) Identify the candidate key(s) of R based on the Functional Dependencies. You need to use the concept of attribute closure to identify the key(s). Intermediate steps in this process should be detailed.

(c) Assume that R is in 1NF. Now normalise the relation to 2NF, 3NF, and BCNF. Be sure to indicate the FDs you are removing at each step, and why. Just giving the decompositions in each of the three Normal Forms is not sufficient.

Please kindly note that for Question(c) the full mark will only be given to the fully correct normalization result. If you get some functional dependency wrong in Question(a), then some partial marks will be deducted for both the functional dependencies and the possibly incorrect normalization result. Given this, it is very important to get the functional dependencies right in the first instance. While it is recommended to answer this question on just one page, you should use no more than two pages for this question.