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Question Number 157725 by joki last updated on 27/Oct/21

$$\mathrm{form}\mathrm{f}(\mathrm{x},\mathrm{y},\mathrm{z})={\left({\left(\mathrm{xy}\right)}^{\prime }\mathrm{c}\right)}^{\prime }{\left(({\mathrm{x}}^{\prime }+\mathrm{c})({\mathrm{y}}^{\prime }+{\mathrm{z}}^{\prime })\right)}^{\prime }$$$$\mathrm{in}\mathrm{standard}\mathrm{SOP}\mathrm{form}\mathrm{and}\mathrm{canonical}\mathrm{SOP}\mathrm{form}$$

Answered by Kunal12588 last updated on 27/Oct/21

$${\left[{\left(xy\right)}^{\prime }c\right]}^{\prime }{\left[(x^{\prime }+c)(y^{\prime }+z^{\prime })\right]}^{\prime }$$$$=[{\left({\left(xy\right)}^{\prime }\right)}^{\prime }+c^{\prime }][{(x^{\prime }+c)}^{\prime }+{(y^{\prime }+z^{\prime })}^{\prime }]$$$$=(xy+c^{\prime })({xc}^{\prime }+yz)$$$$={xyc}^{\prime }+xyz+{xc}^{\prime }+{yzc}^{\prime }$$$$={xc}^{\prime }(y+1)+xyz+{yzc}^{\prime }$$$$SSOP={xc}^{\prime }+xyz+{yzc}^{\prime }$$$$CSOP={xc}^{\prime }(y+y^{\prime })(z+z^{\prime })+xyz(c+c^{\prime })+{yzc}^{\prime }(x+x^{\prime })$$$$={xyzc}^{\prime }+{xyz}^{\prime }{c}^{\prime }+{xy}^{\prime }{zc}^{\prime }+{xy}^{\prime }{z}^{\prime }{c}^{\prime }+xyzc+x^{\prime }{yzc}^{\prime }$$

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