I was going to post this yesterday, but thought I understood it ... and now I don't:
In Schaum's Probability, Random Variables, & Random Processes by Hwei Hsu, problem 1.11 gives four switched circuit diagrams, each with 3 switches. The goal is to define the path from to . The text says:
Consider the switching networks shown in Fig. 1-5. Let , , and denote the events that the switches , , and are closed, respectively. Let denote the event that there is a closed path between terminals and . Express in terms of , , and for each of the networks shown.
The two networks I'm concerned with are (a) and (b), which simply have the switches in series and parallel, respectively. The answers given are:
This doesn't make sense to me. It is true that in (a), all switches must be switched, and I would agree that (in fact, that was my answer to the problem) but I don't see how unless . Problem (b) has a similar issue.
Is the book wrong or do I not understand the intersection and union ( / ) correctly?