Just as there are basic examples of groups, such as the group Z of integers and the permutation group Sn of permutations of n objects, there are also basic examples of Boolean algebra such as the following. The algebra of binary digits or bits 0 and 1 under the logical operations including disjunction, conjunction, and negation. Applications include the propositional calculus and the theory of digital circuits.

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  • Just as there are basic examples of groups, such as the group Z of integers and the permutation group Sn of permutations of n objects, there are also basic examples of Boolean algebra such as the following. The algebra of binary digits or bits 0 and 1 under the logical operations including disjunction, conjunction, and negation. Applications include the propositional calculus and the theory of digital circuits. The algebra of sets under the set operations including Union (set theory)union, intersection, and complement. Applications include any area of mathematics for which sets form a natural foundation of mathematicsfoundation. Boolean algebra thus permits applying the methods of abstract algebra to mathematical logic, digital logic, and the set-theoretic foundations of mathematics. Unlike Group (mathematics)groups of finite order (group theory)order, which exhibit complexity and diversity and whose first-order logicfirst-order theory is decidable only in special cases, all finite Boolean algebras share the same theorems and have a decidable first-order theory. Instead the intricacies of Boolean algebra are divided between the structure of infinite algebras and the algorithmic complexity of their syntaxsyntactic structure.
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  • Just as there are basic examples of groups, such as the group Z of integers and the permutation group Sn of permutations of n objects, there are also basic examples of Boolean algebra such as the following. The algebra of binary digits or bits 0 and 1 under the logical operations including disjunction, conjunction, and negation. Applications include the propositional calculus and the theory of digital circuits.
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  • Boolean algebras canonically defined
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