There are seven candidates hired by Haier: F, G, H, I, W, X and Y, of which one needs to be assigned to the public relations department, three to the production department and three to the sales department. The personnel allocation of these seven employees must meet the following conditions: (1) H and Y must be assigned to the same department. (2) F and G cannot be assigned to the same department. (3) if X is assigned to the sales department, W is assigned to the production department. (4) F must be assigned to the production department.
The pair G and I cannot be assigned to the sales department.