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Session 2793

Enhanced Learning of Boolean Reduction Using Set Theory

John R. Hackworth

Old Dominion University

I. Introduction

Although most students are taught set theory at a very early age, no texts covering Boolean algebra utilize this knowledge to enhance students’ abilities to grasp the concepts of the reduction of Boolean algebraic expressions at the college or university level. This paper explains the one-to-one relationship between Boolean algebra and set theory, and how the students’ prior acquired knowledge of set theory can be leveraged in the classroom as an instructional tool to better teach the reduction of Boolean algebraic expressions.

It is important to stress that this teaching method is not recommended by the author as a substitute for a thorough understanding of the Boolean postulates and theorems required to reduce and solve complex Boolean expressions. Instead, it is used to show the students an alternate way to quickly perform Boolean reduction under certain circumstances. This teaching method is presently used at Old Dominion University in the Electrical Engineering Technology senior elective course EET420 Advanced Logic Design. In the prerequisite for this course, EET310 Digital Electronics, the students receive thorough instruction and practice in the use of Boolean postulates and theorems to perform Boolean reduction and solve Boolean expressions.

II. Discussion

The Boolean AND ( a ib ), OR ( a + b ), INVERT ( a ), logical false (0), and logical true (1), correspond directly to the set theory intersection ( a ∩ b ), union ( a ∪ b ), inversion ( a ), empty set ( φ ), and universal set ( U ). This allows for quick and simple reduction of Boolean expressions containing complex operations that can be easily grasped by students. Many complex switching function problems can be solved faster and easier using set operations rather than classical Boolean algebraic methods.

Consider the pair of Boolean switching functions

f1 (a, b, c) = Σm(0,1, 2, 7)

and "Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright © 2002, American Society for Engineering Education"

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Hackworth, J. (2002, June), Enhanced Learning Of Boolean Reduction Using Set Theory Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--10126