For a finite set $,$ define the sumset $+$ to be the set

$+=\{+$:$,$ in $\}.$

$($a$)[2$ points$]$ For the set $=\{3,1,4\},$ write down the elements of $+($be sure to omit duplicate elements$).$

$($b$)[6$ points$]$ Show that $|+|>=2||1.$

$($c$)[2$ points$]$ Give an example of $$ with $||>=5$ such that $|+|=2||1.$