9. Component i is said to be relevant to the system if for some state vector x,

φ(1i , x) = 1, φ(0i , x) = 0 Otherwise, it is said to be irrelevant.

(a) Explain in words what it means for a component to be irrelevant.

(b) Let A1, . . . ,As be the minimal path sets of a system, and let S denote the set of components. Show that S = si =1 Ai if and only if all components are relevant.

(c) Let C1, . . . ,Ck denote the minimal cut sets. Show that S = ki =1 Ci if and only if all components are relevant.

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