Problem $5.$ Activation Set Suppose we have a set of items I $=\{$i$1,...,$ in$\}$ and k subsets S$1,...,$ Sk$,$ where $$j in $\{1,...,$ k$\},$ Sj $$ I. Some A $$ I is said to $$activate$$ all of the k subsets if $$j in $\{1,...,$ k$\},$ A $$ Sj $=.$ We call such an A an activation set. The Activation$-$Set problem asks: Given such k subsets of I, and an integer d$,$ does there exist an activation set A $$ I such that $|$A$|$ d$?$ Prove Activation$-$Set is NP$-$Complete