Consider the following system. a$)$ Analyse the system in subsystems and through this analysis show that its structure function can be written b$)$ Calculate the reliability of the system if its components operate independently with reliabilities: c$)$ Calculate the reliability significance of components $8$ and $12$ and compare them. d$)$After determining the minimal path sets of the system, use them to give a lower and an upper bound on the reliability of the system if its components operate independently with a common reliability p $=0\mathrm{.}9.$