Boolean Algebra - Mathematics and Statistics for the Environment - page 211

9 Boolean Algebra
A•(B+C)=(A•B)+(A•C)
A + B = B + A
A+(B•C)=(A+B)•(A+C)
A•B=B•A
For the [environmental health] practitioner, total hazard elimination is a noble goal. Yet, as long as the
human element is present in the system, perfection will be impossible to attain. The recognition that
hazards exist at different degrees of severity and accident causation leads to the concept of eliminating
the most “important” hazards first. Thus an evaluation to determine the important of hazards is essen-
tial if there is to be any boundary whatsoever on the problem.
—Brown (1976)
9.1 WHY BOOLEAN ALGEBRA? *
Environmental health practitioners (along with just about everyone else) intuitively know that no
rational person wants to cause pain or injury either to him- or herself or to their fellow humans. The
continuing occurrence of environmental accidents (and other types of accidents) despite the obvious
lack of intent indicates that there is a logical flaw in some part of the reasoning process. No doubt
you have heard the old saying, “The best laid plans …,” and so forth and so on. Simply, when an
environmental accident occurs, a breakdown in the cause-and-effect reasoning process is apparent.
In this chapter, the goal is to describe a basic procedure for evaluating the logical reasoning process
(system safety analysis) commonly used by environmental practitioners involved primarily in occu-
pational health and safety and industrial hygiene activities.
The methodology we briefly describe is based on the concepts of Boolean algebra. One might
ask, “Why describe the basic concepts of Boolean algebra?” The simple answer is that environ-
mental health practitioners are expected to use the tools of logic to mitigate hazardous situations;
Boolean algebra is one of these tools. The compound answer is that environmental health practitio-
ners are often expected to know the basics of Boolean algebra to score well on certification exami-
nations for licensure, or they are taught Boolean algebra concepts in formalized training programs
or on-the-job training. Moreover, Boolean algebra plays an instrumental role in probability theory
and reliability and in various environmental engineering and environmental health studies.
Having evolved in the 1950s, Boolean algebra is a branch of mathematics (a variant of algebra)
that was developed systematically, because of its applications to logic, by the English mathematician
George Boole. Closely related are its applications to sets and probability. A set is any well-defined
list or collection of objects (elements). Usually, sets are denoted by capital letters such as A, B, and
C and their elements by the lower case letters such as e, f, and g. Boolean algebra also underlies the
theory of relations. The most prominent use of Boolean algebra is in the design of electronic switch-
ing circuits used in digital computers (Marcus, 1967). Its original application, however, was in the
* The material presented in this chapter is adapted from Spellman, F.R. and Whiting, N.E., The Handbook of Safety
Engineering: Principles and Applications , Government Institutes Press, Lanham, MD, 2010.
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