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Question Number 197040 by peter frank last updated on 06/Sep/23

Commented by TheHoneyCat last updated on 08/Sep/23

$$a)$$$$Q=XY+\overline{XZ}+YZ$$$$=(X+\overline{X})(XY+\overline{XZ}+YZ)$$$$=(XY+XYZ)+(\overline{XZ}+\overline{XYZ})$$$$=\left(X(Y+YZ)\right)+\left(\overline{X}(Z+YZ)\right)$$$$=\left(XY\right)+\left(\overline{XZ}\right)$$$$=XY+\overline{XZ}$$$$$$$$\mathrm{OR}[\mathrm{AND}[X,Y],\mathrm{AND}[\mathrm{NOT}\left[X\right],Z]]$$

Commented by TheHoneyCat last updated on 08/Sep/23

$$b)$$$$Q=XY+XZ+Y(Y+Z)+XY$$$$=XY+XZ+Y(Y+Z)$$$$=XY+XZ+YY+YZ$$$$=XY+XZ+Y+YZ$$$$=XY+XZ+Y$$$$=XZ+Y$$$$$$$$\mathrm{OR}[Y,\mathrm{AND}[X,Z]]$$

Commented by TheHoneyCat last updated on 08/Sep/23

$$c)$$$$\mathrm{let}W:=X+Y$$$$Q=W(W+Z)$$$$=W+WZ$$$$=W$$$$=X+Y$$$$$$$$\mathrm{OR}[X,Y]$$

Commented by TheHoneyCat last updated on 08/Sep/23

$$d)$$$$\mathrm{let}W:=XY$$$$Q=W+WZ+W\overline{Z}$$$$=W$$$$=XY$$$$$$$$\mathrm{AND}[X,Y]$$

Commented by peter frank last updated on 10/Sep/23

$$\mathrm{thank}\mathrm{you}$$

Commented by TheHoneyCat last updated on 11/Sep/23

you're welcome

Answered by TheHoneyCat last updated on 08/Sep/23

$$e)$$$$Q=X\overline{Y}$$$$$$$$\mathrm{AND}[X,\mathrm{NOT}\left[Y\right]]$$

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