Useful laws and theorems (con’t)
Absorption: X+X•Y=X Dual: X•(X+Y)=X
Absorption (#2): (X+Y')•Y=X•Y Dual: (X•Y')+Y=X+Y
de Morgan's: (X+Y+...)'=X'•Y'•... Dual: (X•Y•...)'=X'+Y'+...
Generalized deM's: f '(X1,X2,...,Xn,0,1,+,•) = f (X1',X2',...,Xn',1,0,•,+)
Duality: (X+Y+...)D=X•Y•... Dual: (X•Y•...)D=X+Y+...
Generalized duality: f D(X1,X2,...,Xn,0,1,+,•)=f (X1,X2,...,Xn,1,0,•,+)
Multiplying & factoring: (X+Y)•(X'+Z)=X•Z+X'•Y
Dual: X•Y+X'•Z=(X+Z)•(X'+Y)
Consensus: (X•Y)+(Y•Z)+(X'•Z)= X•Y+X'•Z
Dual: (X+Y)•(Y+Z)•(X'+Z)=(X+Y)•(X'+Z)