4. In a project selection model, eight projects, numbered 1, 2, ... 8, are in consideration. The following conditions are given. You are required to write constraints to satisfy each of them.

(a) Only one of the projects 3 and 8 has to be selected.

(b) If only project 4 is selected that the project 7 can be selected, but if project 4 is selected then project 7 may or may not be selected.

(c) Not more than two of the projects 1, 3, 5, and 8 may be selected.

(d) Identical decision is required in respect of projects 3 and 6.

(e) Not more than 4 and no less than 2 of the projects 1, 2, 4, 5, 6, and 8 may be selected.

(f) Exactly five of the projects are to be selected.