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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

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  • $\begingroup$ 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. $\endgroup$
    – greybeard
    Oct 27, 2020 at 5:42
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    $\begingroup$ You incorrectly applied duality, you must also negate $A$ and $B$. $\endgroup$ Nov 25, 2020 at 11:37

2 Answers 2

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$$\overline{A+B}=\overline A\cdot\overline B$$

and

$$\overline{A\cdot B}=\overline A+\overline B$$

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

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