Every generalized Boolean algebra is also a BoolRng
, with
multiplication defined as and
and addition defined as xor
.
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
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).
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).
Logical exclusive or, set-theoretic symmetric difference.
Logical exclusive or, set-theoretic symmetric difference.
Defined as a\b ∨ b\a
.
Every Boolean rng gives rise to a Boolean algebra without top:
times
) corresponds toand
;plus
) corresponds toxor
;a or b
is then defined asa xor b xor (a and b)
;a\b
is defined asa xor (a and b)
.BoolRng.asBool.asBoolRing
gives back the originalBoolRng
.algebra.lattice.GenBool.asBoolRing