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Boolean Algebra

Applications

The usefulness of Boolean algebra comes from the fact that its rules can be shown to apply to logical statements. A logical statement, or proposition, can either be true or false, just as an equation with real numbers can be true or false depending on the value of the variable. In Boolean algebra, however, variables do not represent the values that make a statement true, instead they represent the truth or falsity of the statement. That is, a Boolean variable can only have one of two values. In the context of symbolic logic these values are true and false. Boolean algebra is also extremely useful in the field of electrical engineering. In particular, by taking the variables to represent values of on and off (or 0 and 1), Boolean algebra is used to design and analyze digital switching circuitry, such as that found in personal computers, pocket calculators, cd players, cellular telephones, and a host of other electronic products.

Resources

Books

Christian, Robert R. Introduction to Logic and Sets. Waltham, MA: Blaisdell Publishing Co., 1965.

Garfunkel, Soloman A., ed. For All Practical Purposes: Introduction to Contemporary Mathematics. New York: W. H. Freeman, 1988.

Hoernes, Gerhard E., and Melvin F. Heilweil. Boolean Algebra and Logic Design. New York: McGraw Hill, 1964.

Ryan, Ray, and Lisa A. Doyle. Basic Digital Electronics, 2nd ed. Blue Ridge Summit, PA: Tab Books, 1990.

J.R. Maddocks

KEY TERMS

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Binary operation: —A binary operation is a method of combining the elements of a set, two at a time, in such a way that their combination is also a member of the set.
Complement: —The complement of a set, S, written S', is the set containing those members of the universal set that are not contained in S.
Element: —Any member of a set. An object in a set.
Intersection: —The intersection of two sets is itself a set comprised of all the elements common to both sets.
Set: —A set is a collection of things called members or elements of the set. In mathematics, the members of a set will often be numbers.
Set theory: —Set theory is the study of the properties of sets and subsets, especially those properties that are independent of the particular elements in a set.
Subset: —A set, S, is called a subset of another set, I, if every member of S is contained in I.
Union: —The union of two sets is the set that contains all the elements found in one or the other of the two sets.
Universal set: —The universal set is the set containing all the elements being considered.

Additional topics

Science EncyclopediaScience & Philosophy: Bilateral symmetry to Boolean algebraBoolean Algebra - Properties Of Sets, Properties Of Boolean Algebra, Applications