A mathematical model for system requirements analysis (SRA) is developed utilizing elementary set theory. The model provides a means to explicitly treat unwanted or unexpected conditions that may be experienced by the system being analyzed. The SRA model can also be used to derive completeness criteria for the development of system states, as well as the completeness of the SRA itself. The requirement antecedents (the “under what conditions” for each function and performance requirement) are categorized in accordance with their associated consequences. Although generally applicable, the model finds its highest utility in the area of software requirements because of their unique design processes which focus on system states. As such, a relationship with software development “formal methods” is described.