Originally Posted by

**malweth** 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 $\displaystyle a$ to $\displaystyle b$. The text says:

Consider the switching networks shown in Fig. 1-5. Let $\displaystyle A_1$, $\displaystyle A_2$, and $\displaystyle A_3$ denote the events that the switches $\displaystyle s_1$, $\displaystyle s_2$, and $\displaystyle s_3$ are closed, respectively. Let $\displaystyle A_{ab}$ denote the event that there is a closed path between terminals $\displaystyle a$ and $\displaystyle b$. Express $\displaystyle A_{ab}$ in terms of $\displaystyle A_1$, $\displaystyle A_2$, and $\displaystyle A_3$ 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) $\displaystyle A_{ab} = A_1 \cap A_2 \cap A_3$

(b) $\displaystyle A_{ab} = A_1 \cup A_2 \cup A_3$

This doesn't make sense to me. It is true that in (a), all switches must be switched, and I would agree that $\displaystyle A_{ab} = \{A_1A_2A_3\}$ (in fact, that was my answer to the problem) but I don't see how $\displaystyle \{A_1A_2A_3\} = A_1 \cap A_2 \cap A_3$ unless $\displaystyle A_1 = A_2 = A_3$. Problem (b) has a similar issue.

Is the book wrong or do I not understand the intersection and union ($\displaystyle \cap$/$\displaystyle \cup$) correctly?