Question Number 157725 by joki last updated on 27/Oct/21
$$\mathrm{form}\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\left(\left(\mathrm{xy}\right)'\mathrm{c}\right)'\left(\left(\mathrm{x}'+\mathrm{c}\right)\left(\mathrm{y}'+\mathrm{z}'\right)\right)'\: \\ $$$$\mathrm{in}\:\mathrm{standard}\:\mathrm{SOP}\:\mathrm{form}\:\mathrm{and}\:\mathrm{canonical}\:\mathrm{SOP}\:\mathrm{form} \\ $$
Answered by Kunal12588 last updated on 27/Oct/21
![[(xy)′c]′[(x′+c)(y′+z′)]′ =[((xy)′)′+c′][(x′+c)′+(y′+z′)′] =(xy+c′)(xc′+yz) =xyc′+xyz+xc′+yzc′ =xc′(y+1)+xyz+yzc′ SSOP=xc′+xyz+yzc′ CSOP=xc′(y+y′)(z+z′)+xyz(c+c′)+yzc′(x+x′) =xyzc′+xyz′c′+xy′zc′+xy′z′c′+xyzc+x′yzc′](Q157777.png)
$$\left[\left({xy}\right)'{c}\right]'\left[\left({x}'+{c}\right)\left({y}'+{z}'\right)\right]' \\ $$$$=\left[\left(\left({xy}\right)'\right)'+{c}'\right]\left[\left({x}'+{c}\right)'+\left({y}'+{z}'\right)'\right] \\ $$$$=\left({xy}+{c}'\right)\left({xc}'+{yz}\right) \\ $$$$={xyc}'+{xyz}+{xc}'+{yzc}' \\ $$$$={xc}'\left({y}+\mathrm{1}\right)+{xyz}+{yzc}' \\ $$$${SSOP}={xc}'+{xyz}+{yzc}' \\ $$$${CSOP}={xc}'\left({y}+{y}'\right)\left({z}+{z}'\right)+{xyz}\left({c}+{c}'\right)+{yzc}'\left({x}+{x}'\right) \\ $$$$={xyzc}'+{xyz}'{c}'+{xy}'{zc}'+{xy}'{z}'{c}'+{xyzc}+{x}'{yzc}' \\ $$