By translating teaching and learning styles into propositional logic, we have established the foundational knowledge needed for the development of a "smart" computerized tutoring program. Here, we use set theory to explore the act of learning and, with statements in terms of propositional logic and with diagrams, we construct many di erent models of teachers and students. It is stressed that programs resulting from any future projects using this concept would seek not to replace human teachers, who are a necessity for society, but to bene t all involved in the world of education. the application of technology to this work would greatly enhance communication between student and teacher, facilitate the student's understanding of material, and give the student more time in an assisted-learning environment without the usual strain on time or resources.