PPT Slide
Axioms and theorems of Boolean algebra (cont'd)
Useful axioms and theorems of Boolean algebra (continued):
- distributivity: 8. X • (Y + Z) = (X • Y) + (X • Z) 8D. X + (Y • Z) = (X + Y) • (X + Z)
- uniting: 9. X • Y + X • Y' = X 9D. (X + Y) • (X + Y') = X
- absorption: 10. X + X • Y = X 10D. X • (X + Y) = X
- a second form of absorption: 11. (X + Y') • Y = X • Y 11D. (X • Y') + Y = X + Y
- de Morgan's: 12. (X + Y + ...)' = X' • Y' • ... 12D. (X • Y • ...)' = X' + Y' + ...
- generalized de Morgan's: 13. f'(X1,X2,...,Xn,0,1,+,•) = f(X1',X2',...,Xn',1,0,•,+)