Recall that a Linear Threshold Function $($LTF$)$ is any Boolean function f : $\{1\}$n $\{1\}$

of the form f $($x$)=$ sgn$($w $$ x $$ $),$ where w $=($w$1,...,$ wn$)$ in Rn is a weight vector and in R

is known as a threshold. Here we will consider the subclass of LTFs for which $=0$ and each

wi$,1$ i $$ n$,$ is restricted to be an integer between $$n and n$.$ Let C$[$n$]$ be this subclass of

LTFs$.$ Show that the VC dimension of C$[$n$]$ is $($n$).$