Axioms and theorems of Boolean algebra (cont’)
Duality
- a dual of a Boolean expression is derived by replacing • by +, + by •, 0 by 1, and 1 by 0, and leaving variables unchanged
- any theorem that can be proven is thus also proven for its dual!
- a meta-theorem (a theorem about theorems)
duality: 16. X + Y + ... ? X • Y • ...
generalized duality: 17. f (X1,X2,...,Xn,0,1,+,•) ? f(X1,X2,...,Xn,1,0,•,+)
Different than deMorgan’s Law
- this is a statement about theorems
- this is not a way to manipulate (re-write) expressions