Boolean algebra

Boolean algebra, introduced by George Boole in 1847, is the subarea of algebra in which the values of the variables are the truth values false and true. Instead of elementary algebra (where the values of the variables are numbers and the main operations are addition and multiplication), the main operations of Boolean algebra are the conjunction AND, the disjunction OR and the negation NOT. It is used for describing logical relations in the same way that ordinary algebra describes numeric relations.
Boolean algebra has been fundamental in the development of digital electronics.


LawAND formOR form
IdentifyA * = AA + = A
Zero and OneA * = A + =
InverseA * A = A + A =
IdempotentA * A = AA + A = A
CommutativeA * B = B * AA + B = B + A
AssociativeA * (B * C) = (A * B) * CA + (B + C) = (A + B) + C
DistributiveA + (B * C) = (A + B) * (A + C)A * (B + C) = (A * B) + (A * C)
AbsorptionA * (A + B) = AA + (A * B) = A
De Morgan'sA * B = A + BA + B = A * B
Double Compl.A = A