Akademik

A Boolean algebra is a system consisting of a set S and two operations, n and ? (cap and cup), subject to the following axioms. For all sets a,b,c, that are members of S:

1 a n (b n c) = (a n b) n c.

Also a ? (b ? c) = (a ? b) ? c (associativity)

2 a n b = b n a.

Also a ? b = b ? a (commutativity)

3 a n (b ? c) = (a n b) ? (a n c).

Also a ? (b n c) = (a ? b) n (a ? c) (distributivity)

4 There belong to S two elements, 0 and 1, with the properties a ? 0 = a; a n 1 = a (identity)

5 For each set a in S there exists a set a' with the properties that a ? a' = 1, a n a' = 0 (complementation).

The propositional calculus can be represented as a Boolean algebra, with n representing &, ? representing ∨, and 1 = T, 0 = F. The Boolean operators are then the truth functors, such as &, ∨, and ¬. A Boolean search is a search for things meeting a condition defined with these operators.