Axioms and theorems of Boolean algebra (contd)
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 11. (X + Y') Y = X Y 11D. (X Y') + Y = X + Y
factoring: 12. (X + Y) (X' + Z) = 16D. X Y + X' Z = X Z + X' Y (X + Z) (X' + Y)
concensus: 13. (X Y) + (Y Z) + (X' Z) = 17D. (X + Y) (Y + Z) (X' + Z) = X Y + X' Z (X + Y) (X' + Z)