Consider the following relational database schema relating to physician treating patients. The primary keys are underlined. The foreign keys are self-explanatory.

PHYSICIAN (P_id, Name, Specialty, Hospital, Address)

TREATS (P_id, Pt_id, Date_last_treated)

PATIENT (Pt_id, Pname, Address, DoB)

Translate each of the following statements into an expression of relational algebra.

(i) Display name of doctors who treated more than 400 patients living in Vellore area. [3 Marks]

(ii) Display name of patients who had been treated by doctors of all specialty. [3 Marks]

(iii) Display name of patients who were never treated by pulmonologist. [2 Marks]

(iv) Display name of patients born after January 31, 1990 and the name and specialty of doctors who treated them. [2 Marks]