Discussion Question Essay Example | Topics and Well Written Essays - 250 words - 18

Discussion Question - Essay Example A conjunction, disjunction, negation or ordering relation is all naturally available in practical examples so that it is basic to make use of this relationship. General approaches from duality can also be applied in order theory to Boolean algebras. The order dual of every Boolean algebra obtained by interchanging AND and OR is also a Boolean algebra. By interchanging 0 with 1, the law that applies to Boolean algebras can be changed into another valid dual law. Each Boolean algebra (A, AND, OR) produces a ring (A,,*) that defines a + b = (a AND b) or (b AND a) and a * b = a AND b. the 0 element of this ring matches the 0 of the Boolean algebra while the multiplicative identity element is the 1 of the Boolean algebra. a *a = a for all the rings in A. such rings are called Boolean rings. On the other hand, given a Boolean ring A, this can be turned into a Boolean algebra by the definition x OR y = x +y + xy and x AND y = xy. We can conclude that every Boolean algebra rises from a Boolean ring and vice versa. Goodstein