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2. Boolean algebra - Wikipedia

   en.wikipedia.org/wiki/Boolean_algebra

   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 ...

3. Boolean algebra (structure) - Wikipedia

   en.wikipedia.org/wiki/Boolean_algebra_(structure)

   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.

4. List of Boolean algebra topics - Wikipedia

   en.wikipedia.org/wiki/List_of_Boolean_algebra_topics

   Download as PDF; Printable version; In other projects ... This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and ...

5. Boolean function - Wikipedia

   en.wikipedia.org/wiki/Boolean_function

   In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.

6. Complete Boolean algebra - Wikipedia

   en.wikipedia.org/wiki/Complete_Boolean_algebra

   For a complete boolean algebra infinite de-Morgan's laws hold. A Boolean algebra is complete if and only if its Stone space of prime ideals is extremally disconnected. Sikorski's extension theorem states that if A is a subalgebra of a Boolean algebra B, then any homomorphism from A to a complete Boolean algebra C can be extended to a morphism ...

7. List of set identities and relations - Wikipedia

   en.wikipedia.org/wiki/List_of_set_identities_and...

   3.1 Formulas for binary set operations ⋂, ... Download as PDF; Printable version; ... show that it is a Boolean algebra. ...

8. Boolean algebras canonically defined - Wikipedia

   en.wikipedia.org/wiki/Boolean_algebras...

   Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...

9. Two-element Boolean algebra - Wikipedia

   en.wikipedia.org/wiki/Two-element_Boolean_algebra

   In a four-element Boolean algebra whose domain is the powerset of ⁠ {,} ⁠, this formula corresponds to the statement (x = ∅) ∨ (x = {0,1}) and is false when x is ⁠ {} ⁠. The decidability for the first-order theory of many classes of Boolean algebras can still be shown, using quantifier elimination or small model property (with the ...