2-31
COMMUTATIVE LAW the order in which terms are written does not affect their value (AB =
BA, A+B = B+A).
ASSOCIATIVE LAW a simple equality statement A(BC) = ABC or A+(B+C) = A+B+C.
IDEMPOTENT LAW a term ANDed with itself or ORed with itself is equal to that term (AA =
A, A+A = A).
DOUBLE NEGATIVE LAW a term that is inverted twice is equal to the term A = A.
COMPLEMENTARY LAW a term ANDed with its complement equals 0, and a term ORed
with its complement equals 1 (A A = 0, A+ A = 1).
LAW OF INTERSECTION a term ANDed with 1 equals that term and a term ANDed with 0
equals 0 (A·1 = A, A·0 = 0).
LAW OF UNION a term ORed with 1 equals 1 and a term ORed with 0 equals that term (A+1 =
1, A+0 = A).
DeMORGAN’S THEOREM this theorem consists of two parts: (1) AB = A + B and (2)
B
A +
= A · B (Look at the fourth and eighth sets of gates in table 2-4).
DISTRIBUTIVE LAW (1) a term (A) ANDed with an parenthetical expression (B+C) equals
that term ANDed with each term within the parenthesis: A·(B+C) = AB+AC; (2) a term (A) ORed with a
parenthetical expression ( B ·C) equals that term ORed with each term within the parenthesis: A+(BC) =
(A+B) · (A+C).
LAW OF ABSORPTION this law is the result of the application of several other laws: A·(A+B)
= A or A+(AB) = A.
LAW OF COMMON IDENTITIES the two statements A·( A +B) = AB and A+ A B = A+B are
based on the complementary law.
