Boolean Algebra - Laws

Laws

A law of Boolean algebra is an equation such as x∨(yz) = (xy)∨z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡, but such extensions are unnecessary for the purposes to which the laws are put. Such purposes include the definition of a Boolean algebra as any model of the Boolean laws, and as a means for deriving new laws from old as in the derivation of x∨(yz) = x∨(zy) from yz = zy as treated in the section on axiomatization.

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