10. Let ti denote the time of failure of the ith component; let (t) denote the time...

10. Let ti denote the time of failure of the ith component; let τφ(t) denote the time to failure of the system φ as a function of the vector t = (t1, . . . , tn). Show that max 1js min i∈Aj ti = τφ(t) = min 1jk max i∈Cj ti where C1, . . . ,Ck are the minimal cut sets, and A1, . . . ,As the minimal path sets.