Question #$1[12$ points$]$:

Compute the weakest precondition for each of the following:

$1.$

x $=$ x $-2$;

z $=$ x $+1$;

$\{$ z $!=0\}$

$2.$

$3.$

x $=2*$ y;

z $=$ x $+$ y;

$\{$ z $>0\}$

w $=2*$ w;

z $=-$w;

y $=$ v $+1$;

x $=$ min$($y$,$ z$)$;

$\{$ x $<0\}$