$($a$)(10$ points$)$ Is the current state safe or not? Justify your answer. $($b$)(10$ points$)$ Suppose P$3$ requests for $6$ units of R$1.$ Will this request be granted or refused? Justify your answer. $($c$)(20$ points$)$ While the original Banker$$s algorithm assumes a fixed number of processes, we can still apply it in case of limited changes. Let us consider a new process, P$4,$ arrives with a maximum resource claim of $[4,2,3]$ for the three types of resources. Now suppose P$4$ requests $3$ units of R$3.$ Should the request be granted or refused? Justify your answer. $($This question is independent of $($b$)).$