## Algebra## Abstract Algebra |

## What is Boolean algebra? |

Boolean algebra is an abstract mathematical system used to express the relationship between sets (groups of objects or concepts; see “Math Basics”). It is important in the study of information theory, the theory of probability, and the geometry of sets. The use of Boolean notation in electrical networks aided the development of switching theory and the eventual design of computers.

It was English mathematician George Boole (1815–1864) who first developed this type of logic by demonstrating the algebraic manipulation of logical statements, showing whether or not a statement is true, and showing how a statement can be made into a simpler, more convenient form without changing its overall meaning. Today, this way of looking at logic is called Boolean algebra. (For more information about Boole, see “History of Mathematics.”)

Boolean algebra did not end there: In 1881, the English logician and mathematician John Venn (1834–1923) interpreted Boole’s work and introduced a new way of diagramming Boole’s notation in his treatise, *Symbolic Logic.* This was later refined by the English mathematician Charles Dodgson (1832–1898), better known as the writer of *Alice’s Adventures in Wonderland* (under the pseudonym Lewis Carroll). Today when studying sets, we call this method not the Boole, Carroll, or Dodgson diagram, but the Venn diagram. Thus, Boolean notation demonstrates the relationship between groups, indicating what is in each set alone, what is jointly contained in both, and what is present in neither.