Question

State and prove De Morgan's theorems.

Answer 1

$De$ $Morga{n}^{\prime }s$ theorem

The complement of the sum of two or more variables is equal to the product of the complement of the variables.

The complement of the product of two or more variables is equal to the sum of complements of variables.

$prove$

$A=0$ $B=1$

$\overline{A+B}=\overline{0+1}=\overline{1}=0$

$\overline{A}.\overline{B}=\overline{0}.\overline{1}=1.0=0$

Hence $\overline{A+B}=\overline{A}.\overline{B}$