9. Component / is said to be relevant to the system if for some state vector x, 0(1;, x) = 1, 0(0,, x) = 0 Otherwise, it is said to be irrelevant.

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

(b) Let Á ÷ , . . . , As be the minimal path sets of a system, and let S denote the set of components. Show that S = Ui=i>l/ if and only if all components are relevant.

(c) Let Cx,..., Ck denote the minimal cut sets. Show that S = Uf= é Q if and only if all components are relevant.