Three components are connected to form a system as shown in

Three components are connected to form a system as shown in Figure 1. Because the components in the 2-3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2-3 subsystem. The experiment consists of determining the condition of each component: S (success) for a functioning component and F (failure) for a nonfunctioning component.

Solution

(a) {SSF,SFS,FSS}

(b) {SSS,SSD,SFS,FSS}

(c) {SSS,SSF,SFS}

(d) C^c means system is not functions so answer is {FSS,SFF,FSF,FFS,FFF}

      AUB means either A either B or Both so answer is {SSF,SFS,SSS,FSS}

      A C means events which are present in both so {SSF,SFS}

   BUC means either B either C or Both so answer is {SSS,SSF,SFS,FSS}

BC means events which are present in both so {SSS,SSF,SFS}