Sentences with boolean algebra
Bool·e·an al·gebra
B b - In Boolean algebra, logical operations are performed by operators such as "and", "or", in a similar way to mathematical signs.These kinds of networks can be analyzed using Boolean algebra by assigning the two states, such as "on"/"off", to the Boolean constants "0" and "1".Boolean algebra is a branch of symbolic logic used in computers.
- The set of divisors of 30, with binary operators: g. c. d. and l. c. m. , unary operator: division into 30, and identity elements: 1 and 30, forms a Boolean algebra. The nodes Ni of a Boolean lattice can be labeled with Boolean formulae F(Ni), such that if node C is the meet of nodes A and B, then F(C) = F(A)F(B); if node C is the join of nodes A and B, then F(C) = F(A)+F(B); if node C is the complement of node A, then F(C) = F(A)'; and the '≤' order relation corresponds to logical entailment. A set of 'n' Boolean formulae could be called a "basis" for a 2n-element Boolean algebra iff they are all mutually disjoint (i. e. , the product of any pair is 0) and their Σ (collective sum) is equal to 1. A set S of formulae could then generate a Boolean algebra inductively as follows: (base step) let P0 = S ∪ {(ΣS)'}, (inductive step) if a pair of formulae F and G in Pi are non-disjoint (i. e. , FG≠0), then let Pi+1 = (Pi ∪ {FG, F'G, FG'}) \ {F, G}, otherwise Pi is a basis. If CARD(Pi)=n then the Boolean algebra will have 2n elements which are all "linear combinations" of the basis elements, with a coefficient of either 0 or 1 for each term of each linear combination.