A misquided mathematician would like to substract term $A\overline{C}$ from both side of equality

$BC+ABD+A\overline{C} = BC + A\overline{C}$

Would they still be equal if he did so justify and simplify the expression.

$F= (X+\overline{Z}) (Z+\overline{WY}) + (VZ+ W\overline{X}) (\overline{Y}+\overline{Z})$

Mumbai University > COMPS > Sem 3 > Digital Logic Design and Analysis

Marks: 10 M

Year: Dec 2014

1. $BC+ABD+A\overline{C} = BC + A\overline{C}$

   Now, misquided mathematician would like to subtract term AC from both the side

   Lets, substract term $A\overline{C}$ from both side of the equality.

   $BC+ABD+A\overline{C}-A\overline{C}=BC+A\overline{C}-A\overline{C}$

   Therefore $BC+ABD+A\overline{C}(1-1)=BC+A\overline{C}(1-1)$

$\hspace{10cm}$ Now(1-1)=0

$BC+ABD=BC\hspace{7cm} A\overline{C}=0$

So, from above, the equations will not be equals anymore if we substracting the term $A\overline{C}$ from both side.

$\boxed{BC+ABD ≠BC}$

1. F= (X+Z) (Z+WY) + (VZ+ WX) (Y+Z)

   = (X+Z) (Z.WY) + (VZ+ WX) (Y.Z) … A+B=A.B

   = (X+Z) [Z.(W+Y)] +VZYZ +WXYZ

   =(X+Z) [WZ+YZ] +0 + WXYZ ….. ZZ=0

   = Z [XW + W + XY + Y + WXY]

   = Z [W(X+1)+ Y(X+1) + WXY]

   = Z [W+Y +WXY] …… X+1=1

   = Z[W+Y(1+WX)]

   =Z[W+Y]

$\boxed{F=Z[W+Y]}$