Question

The Boolean expression
$(X+Y)(X+\overline{Y})+\overline{\left(X\overline{Y}\right)+\overline{X}}$ simplifies to

• A. Y
• B. XY
• C. X
• D. X+Y

Answer 1

The correct option is C X

Let $F=(X+Y)(X+\overline{Y})+\overline{X\overline{Y}+\overline{X}}$
$F=X+X\overline{Y}+XY+\overline{X\overline{Y}}.\overline{\overline{X}}$
$=X+(\overline{X}+Y).X$
$=X+XY$
$=X$