Boolean algebra Basic identities Idempotence: AA=AAA = AAA=A, A+A=AA+A=AA+A=A Commutativity: AB=BAAB = BAAB=BA, A+B=B+AA+B = B+AA+B=B+A Associativity: A(BC)=(AB)C=ABCA(BC) = (AB)C = ABCA(BC)=(AB)C=ABC, A+(B+C)=(A+B)+CA+B+CA+(B+C) = (A+B)+C A+B+CA+(B+C)=(A+B)+CA+B+C Distributivity: A(B+C)=AB+ACA(B+C)= AB+ACA(B+C)=AB+AC, A+(BC)=(A+B)(A+C)A+(BC)= (A+B)(A+C)A+(BC)=(A+B)(A+C) Duality: If C=ABC =ABC=AB, then Cˉ=Aˉ+Bˉ\bar{C} = \bar{A} + \bar{B}Cˉ=Aˉ+Bˉ, if D=A+BD=A+BD=A+B, then Dˉ=AˉBˉ\bar{D} = \bar{A}\bar{B}Dˉ=AˉBˉ