Boolean algebra

:For a basic intro to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic.

Homomorphisms and isomorphisms

A homomorphism between the Boolean algebras A and B is a function f : A → B such that for all a, b in A:

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:f(a lor b) = f(a) lor f(b)

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:f(a land b) = f(a) land f(b)

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:f(0) = 0

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:f(1) = 1

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It then follows that f(¬a) = ¬f(a) for all a in A as well. The class of all Boolean algebras, together with this notion of morphism, forms a category. An isomorphism from A to B is a homomorphism from A to B which is bijective. The inverse of an isomorphism is also an isomorphism, and we call the two Boolean algebras A and B isomorphic. From the standpoint of Boolean algebra theory, they cannot be distinguished; they differ only in the notation of their elements.

Related Topics:
Class - Category - Bijective

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