Mathematics - Sets and Relations Question with Solution | TestHub

$\begin{array}{rl}& A=\{(x,y)\in \mathbf{R}\times \mathbf{R}:|x+y|\ge 3\}\\ & \text{ and }B=\{(x,y)\in \mathbf{R}\times \mathbf{R}:|x|+|y|\le 3\}\\ & C=\{(x,y)\in A\cap B:x=0\text{ or }y=0\}\end{array}$

$A\cap B$ will have only common points lying on the line $PQ$ and $RS$
Now, $C=\{(-3,0),(3,0),(0,3),(0,-3)\}$
${\sum }_{(x,y)\in c}|x+y|=3+3+3+3=12$