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:

(a)

(b)

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?