please check the picture and do

The task: Using the Post$$s Functional Completeness Theorem,

check out if the given system of logical connectivities is complete,

by checking their belonging to the following $5$ classes:

$1)$ Class C$0=$ The class of all $0-$preserving functions;

$2)$ Class C$1=$ The class of all $1-$preserving functions;

$3)$ Class L $=$ The class of all linear functions;

$4)$ Class S $=$ The class of all self$-$dual functions;

$5)$ Class M $=$ The class of all monotonic functions.$\{\stackrel{}{x}+y,xvvy,1\}$