Question Number 1047 by 112358 last updated on 23/May/15
$${Simplify}\:{the}\:{following} \\ $$$${expression}\:{using}\:{the}\:{laws}\:{of}\: \\ $$$${Boolean}\:{algebra}: \\ $$$$\left({x}\wedge\backsim{y}\right)\vee\left(\backsim{y}\wedge\backsim{z}\right)\vee\left(\backsim{x}\wedge\backsim{z}\right)\:. \\ $$$$ \\ $$
Commented by prakash jain last updated on 24/May/15
$$\backsim{x}\wedge\backsim{z}=\backsim\left({x}\vee{z}\right) \\ $$$$\backsim{y}\wedge\backsim{z}=\backsim\left({y}\vee{z}\right) \\ $$$$\left(\backsim\left({y}\vee{z}\right)\right)\vee\left(\backsim\left({x}\vee{z}\right)\right)=\backsim\left(\left({y}\vee{z}\right)\wedge\left({x}\vee{z}\right)\right) \\ $$$$=\backsim\left(\left({y}\wedge{x}\right)\vee{z}\right) \\ $$$$ \\ $$