with n elements has 2n different subsets, including the empty set 0 and I itself ( each 
either belongs to the subset or does not belong). The Boolean algebra Bn consists of these 2n
subsets with the operations of union 
, intersection 
,
and complement - (the complement of X is also written 
).
Examples of rules that are valid for any X,Y,Z are 
Every Boolean equation is equivalent to its dual, in which the operations of union and intersection are interchanged and simultaneously all variables are complemented.
For example, 
is equivalent to 
.
B1 is also called propositional calculus. It is the calculus of truth values (0 = false, I = 1 = true, = or,
= and, - = not).
Boolean variables and operations can be used in high-level programming languages (TRUE, FALSE, OR, AND, NOT, sometimes XOR).
Sometimes the rules of Boolean algebra can also be used to simplify considerably the logic of a complicated sequence of tests.