Boolean algebra is a mathematical system used to solve problems in logic, probability, and engineering. The system is named for George Boole, an English logician and mathematician of the 1800’s.
Boole developed a system of formulating logical statements symbolically. These statements could then be written and proved in a manner similar to that used in ordinary algebra. Boole’s “algebra of logic” also has applications in engineering problems such as the design of electrical switching circuits, particularly circuits that perform arithmetic operations in calculators and computers.
Boolean algebra deals with relationships between sets (groups of ideas or objects). Examples of sets are “numbers less than one hundred,” “red flowers,” and “people.” In Boolean algebra, such sets are represented by the letters A, B, C, and so on. Three basic Boolean operations follow laws similar to those of ordinary algebra. The symbols for these operations are ∩ (“cap” or “intersection”), ∪ (“cup” or “union”), and ′ (“complement”). For example, the operation A ∩ B represents the set of those elements that are in both sets A and B. This relationship can be represented by the shaded portion of the overlapping circles shown in the first diagram. The operations A ∪ B and A′ are represented in similar diagrams. The rectangle in each diagram represents a universal set (symbol I), the totality of all elements being discussed.
