xy + x'z + yz ≡ xy + x'z
De Morgan's laws:
NOT (P OR Q) ≡ (NOT P) AND (NOT Q)
NOT (P AND Q) ≡ (NOT P) OR (NOT Q)
AKA:
(P+Q)'≡P'Q'
(PQ)'≡P'+Q'
AKA:
¬(P U Q)≡¬P ∩ ¬Q
¬(P ∩ Q)≡¬P U ¬Q
Duality Principle:If a given statement is valid for all partially ordered sets, then its dual statement, obtained by inverting the direction of all order relations and by dualizing all order theoretic definitions involved, is also valid for all partially ordered sets. The laws of classical logicPeirce's law:((P→Q)→P)→PP must be true if there is a proposition Q such that the truth of P follows from the truth of "if Pthen Q". In particular, when Q is taken to be a false formula, the law says that if P must be true whenever it implies the false, then P is true.
Stone's representation theorem for Boolean algebras:Every Boolean algebra is isomorphic to a field of sets.
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The prototypical Boolean algebra; i.e. the Boolean algebra defined over the Boolean domain, has two elements in it: 0 and 1. For more information about Boolean algebra, please refer to the related link below.
Most likely it is called BOOLEAN ALGEBRA I.
George Boole invented Boolean algebra.
One use of Boolean algebra is to minimize any function or logic gate.
Algebra is a very broad topic covering all sorts of things, including Boolean algebra. Boolean algebra in itself is the study of a variable called "Boolean." This variable can only take two values: true and false. See 'related links' for more information.