Question

The Boolean expression XY+(X'+Y') Z is equivalent to

• A. $XY{Z}^{\prime }+X^{\prime }{Y}^{\prime }Z$
• B. $X^{\prime }{Y}^{\prime }{Z}^{\prime }+XYZ$
• C. $(X+Z)(Y+Z)$
• D. $(X^{\prime }+Z)(Y^{\prime }+Z)$

Answer 1

The correct option is C $(X+Z)(Y+Z)$

$XY+(\overline{X}+\overline{Y})Z=XY+\overline{XY}Z$
$=(XY+\overline{XY})(XY+Z)$
$=XY+Z$
$=(X+Z)(Y+Z)$