Component i is said to be relevant to the system if for some state vector x, (1i

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 =s i=1Ai if and only if all components are relevant.

(c) Let C1, . . . , Ck denote the minimal cut sets. Show that S =

k i=1Ci if and only if all components are relevant.