Question

A function of Boolean variables, X, Y and Z is expressed in terms of the min-terms as
$F(X,Y,Z)=\sum (1,2,5,6,7)$
Which one of the product of sums given below is equal to the function $F(X,Y,Z)?$

• A. $(\overline{X}+\overline{Y}+\overline{Z}).(\overline{X}+Y+Z).(X+\overline{Y}+\overline{Z})$
• B. $(X+Y+Z).(X+\overline{Y}+\overline{Z}).(\overline{X}+Y+Z)$
• C. $(\overline{X}+\overline{Y}+Z).(\overline{X}+Y+\overline{Z}).(X+\overline{Y}+Z).(X+Y+\overline{Z}).(X+Y+Z)$
• D. $(X+Y+\overline{Z}).(\overline{X}+Y+Z).(\overline{X}+Y+\overline{Z}).(\overline{X}+\overline{Y}+Z).(\overline{X}+\overline{Y}+\overline{Z})$

Answer 1

The correct option is B $(X+Y+Z).(X+\overline{Y}+\overline{Z}).(\overline{X}+Y+Z)$

$F(X,Y,Z)=\sum m(1,2,5,6,7)$
$=\Pi M(0,3,4)$
$=(X+Y+Z).(X+\overline{Y}+\overline{Z}).(\overline{X}+Y+Z)$