Question 1.9: Use Boolean algebra and de Morgan's theorem for two variable...

Introduction to Digital Electronics [EXP-30805]

Use Boolean algebra and de Morgan’s theorem for two variables, $\overline{A+B} =\overline{A}\cdot \overline{B}$ , to show that the form given in Equation 1.16

$\overline{A+B} =\overline{A} \cdot \overline{B} \Rightarrow \overline{A+B+C+...} =\overline{A} \cdot \overline{B} \cdot \overline{C} ...$ for three variables is also true.

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$\overline{A+B+C} =\overline{(A+B)+C}$ associative law

$=\overline{(A+B)} ·\overline{C}$ De Morgan’s theorem

$=(\overline{A}·\overline{B} ) ·\overline{C}$ De Morgan’s theorem

$=\overline{A}·\overline{B} ·\overline{C}$ associative law

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