# Exercise 4

### 1 Tuple Relational Calculus

Based on the Company database from Exercise 1, propose tuple relational calculus expressions that represent the following relation descriptions.
1. The first name of all employees that work in the department whose manager's CPR no. is 654.
2. The CPR no. of all employees that were born before 1961-01-01 and work on project InteractiveTV.
3. The complete names of all employees of department 10 who have to work for more than 15 hours per week on project PalmTop.

### 2 Domain Relational Calculus

Also based on the company database, propose domain relational calculus expressions that represent the following relation descriptions:
1. The number of all departments which have locations that are not allocated any projects.
2. The CPR no. and dates of birth of all employees that are older than the manager of their departments.

### 3 Relational Algebra

Identify relational algebra expressions that represent the relation descriptions of Problems 1 and 2 above. Compute the relations obtained when the algebraic expressions are evaluated on the Company database.

Best regards,
Kristian Torp