2-31COMMUTATIVE LAWthe order in which terms are written does not affect their value (AB =BA, A+B = B+A).ASSOCIATIVE LAWa simple equality statement A(BC) = ABC or A+(B+C) = A+B+C.IDEMPOTENT LAWa term ANDed with itself or ORed with itself is equal to that term (AA =A, A+A = A).DOUBLE NEGATIVE LAWa term that is inverted twice is equal to the term A = A.COMPLEMENTARY LAWa term ANDed with its complement equals 0, and a term ORedwith its complement equals 1 (A A = 0, A+ A = 1).LAW OF INTERSECTIONa term ANDed with 1 equals that term and a term ANDed with 0equals 0 (A·1 = A, A·0 = 0).LAW OF UNIONa term ORed with 1 equals 1 and a term ORed with 0 equals that term (A+1 =1, A+0 = A).DeMORGAN’S THEOREMthis theorem consists of two parts: (1) AB = A + B and (2)BA += 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) equalsthat term ANDed with each term within the parenthesis: A·(B+C) = AB+AC; (2) a term (A) ORed with aparenthetical expression ( B ·C) equals that term ORed with each term within the parenthesis: A+(BC) =(A+B) · (A+C).LAW OF ABSORPTIONthis law is the result of the application of several other laws: A·(A+B)= A or A+(AB) = A.LAW OF COMMON IDENTITIESthe two statements A·( A +B) = AB and A+ A B = A+B arebased on the complementary law.