This study presents a Formal General Design Theory (FGDT), a mathematical theory of design. The scope and objectives of FGDT, as well as modeling design artifacts were examined in the first part of this study. Here, the entire design process (termed also idealized design process) is conceptualized by a single operator which has several properties that immanently characterize the design process. The concept of a generating set for the design solution space is also introduced, and its relation with the axiomatic model of the design process is explored. The FGDT will provide insight into design practice and guidelines for developing CAD systems.