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What is a Boolean algebra?

What is a Boolean algebra? Here are some definitions.

Noun
  1. (algebra) A De Morgan algebra which also satisfies the law of excluded middle and the law of noncontradiction.
  2. (logic) Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
  3. (mathematics) The study of such algebras; Boolean logic, classical logic.
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