GATE Papers >> ECE >> 2018 >> Question No 19

Question No. 19 ECE | GATE 2018

A function $F\left(A,\;B,\;C\right)$ defined by three Boolean variables $A$, $B$ and $C$ when expressed as sum of products is given by

                                                                $ F=\overline A\cdot\overline B\cdot\overline C\;+\;\overline A\cdot B\cdot\overline C\;+\;A+\overline B+\overline C $

where, $ \begin{array}{l}\overline A,\;\overline B\\\end{array} $, and $ \begin{array}{l}\overline C\\\end{array} $ are the complements of the respective variables. The product of sums (POS) form of the function F is


Answer : (C) $ \begin{array}{l}F=\left(A+B+\overline C\right)\cdot\left(A+\overline B+\overline C\right)\cdot\left(\overline A+B+\overline C\right)\cdot\left(\overline A+\overline B+C\right)\cdot\left(\overline A+\overline B+\overline C\right)\\\end{array} $


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