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The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.
All concrete Boolean algebras satisfy the laws (by proof rather than fiat), whence every concrete Boolean algebra is a Boolean algebra according to our definitions. This axiomatic definition of a Boolean algebra as a set and certain operations satisfying certain laws or axioms by fiat is entirely analogous to the abstract definitions of group ...
The Hasse diagram of the free Boolean algebra on two generators, p and q. Take p (left circle) to be "John is tall" and q (right circle)to be "Mary is rich". The atoms are the four elements in the row just above FALSE. The generators of a free Boolean algebra can represent independent propositions. Consider, for example, the propositions "John ...
English: Hasse diagram of the free Boolean algebra with two generators, p and q. Based on File:Hasse2Free.png. Date: 17 March 2017: ... Free Boolean algebra; Metadata.
A Boolean algebra can be interpreted either as a special kind of ring (a Boolean ring) or a special kind of distributive lattice (a Boolean lattice). Each interpretation is responsible for different distributive laws in the Boolean algebra. Similar structures without distributive laws are near-rings and near-fields instead of rings and division ...
1. A boolean algebra is a complemented distributive lattice. (def) 2. A boolean algebra is a heyting algebra. [1] 3. A boolean algebra is orthocomplemented. [2] 4. A distributive orthocomplemented lattice is orthomodular. 5. A boolean algebra is orthomodular. (1,3,4) 6. An orthomodular lattice is orthocomplemented. (def) 7. An orthocomplemented ...