# is duality principle in boolean algebra is true for every expression

Let say A = 1 and B = 1 and then A+B = 1 now by using duality(replacing or gate by and gate and 1 by 0) we can say that, A.B = 0 but this is not 0, because 1.1 = 1, so please anyone clear my misunderstanding here, Thank in advance

• Welcome to COMPUTER SCIENCE @SE. A·B = 0 but this is not 0 How is 0 not 0? Not identical result (1), but equivalent result: 1 replaced by(exchanged with) 0: 0. – greybeard Oct 27 '20 at 5:42
• You incorrectly applied duality, you must also negate $A$ and $B$. – Andrej Bauer Nov 25 '20 at 11:37

Negation gives you $$\overline{A}=0,\overline{B}=0$$, so everything is ok in "and".