Closure System is closed if for every pair of boolean values,

it produces a boolean result.•

Commutativity A binary operator is commutative if

A°B = B°A for all possible values A and B

Associativity A binary operator is associative if

(A ° B) ° C = A ° (B ° C) for all values A, B and C.

Distribution Two binary operators “°” and “%” are

distributive if A °(B % C) = (A ° B) % (A ° C) for all

boolean values A, B and C.

Identity A boolean value I is an identity element

with respect to a operator “°” if A ° I = A.

Inverse A boolean value I is an inverse element

with respect to some binary operator “°”.