Given an undirected graph G $=($V$,$E$),$ the HALF$-$CLIQUE problem is to decide if there is a subset A $$ V of vertices satisfying the following two conditions:

$|$A$|(|$V $|/2)$

$$ For every pair of vertices u$,$ v in A$,$ if u $=$ v$,$ then $($u$,$ v$)$ in E$.$

Show that HALF$-$CLIQUE is in NP$-$complete.

Hint: Reduce from CLIQUE, which is known to be NP$-$complete.