Question II $(20$ points, $5,5,5,5$ points$)$: Consider the following Boolean formula:

$123412324$ f x x x x x x x x x $=()()()$

$1)$ Transform this instance of the Satisfiability problem into an instance of the VERTEX

COVER decision problem using the polynomial transformation that we developed in class.

$2)$ Find a vertex cover of minimum size of the graph in $1).$