Question

Simplify $x+y-\left[x+y-\left\{x+y-\left(\overline{x+y}\right)\right\}\right]$

Answer 1

Consider the given expression.

$x+y-[x+y-\{x+y-\overline{(x+y)}\}]$

$=x+y-[x+y-\{x+y-(-(x+y))\}]$

$=x+y-[x+y-\{x+y+x+y\}]$

$=x+y-[x+y-\{2x+2y\}]$

$=x+y-[x+y-2x-2y]$

$=x+y-[-x-y]$

$=x+y+x+y$

$=2(x+y)$

Hence, this is the answer.