1. Consider the ER schema of relation F= (A, B, C, D, E, F). Knowing that there are the following (func- tional) dependencies: fdl: {A} + {C, E), fd2: {A} + {D}, fd3: {A, B} + {F}. (a) {5 points} Is F in 1NF? If "yes why? If not modify F so as to put it in INF. Let us call F1 the result of this step (b) {10 points} Is F1 in 2NF? If "yes" why? If not modify F1 so as to put it in 2NF. Let us call F2 the result of this step (e) {5 points} Is F2 in 3NF? If "yes why? If not modify F3 so as to put it in 3NF 2. Consider the following schema: Employee = (Ssn, Name, Address) works on = (W_Ssn, W.Dnumber, Since) Department = (Dnumber, Dname, MgrSsn), where MgrSsn is a foreign key corresponding to the Ssn of the employee who manages that department, this is the implicit implementation of 'manages' (!!!). (a) {20 points} Draw the ER diagram corresponding to the given schema (b) (20 points} Use relational algebra formal language to retrieve the address of all employees working in Dnumber=2 (c) Give the catalogue of this database