Question

If the value of $X+Y=1$, then the value of $X⨁Y$ is equal to

• A. $X$
• B. $\overline{X}+\overline{Y}$
• C. $1$
• D. $0$

Answer 1

The correct option is B $\overline{X}+\overline{Y}$

$X⨁Y=\overline{X⨀Y}=\overline{\overline{X}\overline{Y}+XY}$
$=\left(\overline{\overline{X}\overline{Y}}\right)\left(\overline{XY}\right)$
$=(X+Y)(\overline{X}+\overline{Y})$
$=\overline{X}+\overline{Y}$ {$\because X+Y=1$ which is given}