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In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and introductions. Algebra of sets; Boolean algebra (structure)
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 ...
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.
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 ...
As an example consider the formula (x = 0) ∨ (x = 1). This formula is always true in a 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 {} .
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
This is a list of rules of inference, logical laws that relate to mathematical formulae. Introduction Rules ... (16) truth functions of 2 boolean variables ...
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