Commutative: The commutative property says that binary
operations
AND and OR may be applied left to right or right to left. (A AND B is
the same as B AND
A; A OR B is the same as B OR A.)
Associative: The
associative property says that given three Boolean
variables, they may be ANDed or ORed right to left or
left to right.
((A AND B) AND
C is the same as A AND (B AND C); (A OR B) OR
C is the same
as A OR (B OR C).)
Distributive: The
distributive property says that given three Boolean
variables, the first
AND the result of the second OR the third is the
same as the first
AND the second OR the first AND the third. (A
AND (B OR C) =
(A AND B) OR (A AND C). Also, the first OR the
result of second AND
the third is the same as the first OR the second
AND
the result of the first OR the third. (A OR (B AND C) = (A OR
B) AND (A OR
C).)
Identity: The identity
property says that any value A AND the OR
identity always
returns A and that any value A OR the AND identity
always returns A. (A
AND 1 = A; A OR 0 = A.)
Complement: The
complement property says that any value AND the
compliment of that value
equals the OR identity and that any value
OR the
compliment of that value equals the OR identity. (A AND (A’)
= 0; A OR (A’)
= 1.)
DeMorgan’s Law:
DeMorgan’s Law says that the complement of A
AND B is the
same as the complement of A OR the complement of B,
and the
complement of A OR B is the same as the complement of B
AND the
complement of A. ((A AND B)’ = A’ OR B’; (A OR B)’ = A’
AND
B’).)