The operation of relative complement, symbolically often denoted
a\b
(the symbol for set-theoretic difference, which is the
meaning of relative complement in the lattice of sets).
Every generalized Boolean algebra is also a BoolRng
, with
multiplication defined as and
and addition defined as xor
.
This is the lattice with meet and join swapped
This is the lattice with meet and join swapped
Logical exclusive or, set-theoretic symmetric difference.
Logical exclusive or, set-theoretic symmetric difference.
Defined as a\b ∨ b\a
.
Generalized Boolean algebra, that is, a Boolean algebra without the top element. Generalized Boolean algebras do not (in general) have (absolute) complements, but they have relative complements (see GenBool.without).