$($a$)[10$ points$]$ Does this reduction prove that HC is NP$-$Hard if TSP is NP$-$Hard or TSP is NP$-$Hard if HC is NP$-$Hard? Justify your answer. $($b$)[5$ points$]$ Given the reduction $($and details from $($a$))$ can we prove TSP is NPComplete? If so$,$ what is needed? If not, why? $($c$)[5$ points$]$ Given the reduction $($and details from $($a$)),$ can we prove HC is NPComplete? If so$,$ what is needed? If not, why?