3. For any structure function , we define the dual structure by (a) Show that the dual...

3. For any structure function ϕ, we define the dual structure by

(a) Show that the dual of a parallel (series) system is a series (parallel) system.

(b) Show that the dual of a dual structure is the original structure.

(c) What is the dual of a k-out-of-n structure?

(d) Show that a minimal path (cut) set of the dual system is a minimal cut (path) set of the original structure.