Examples of Set Intersection and Set Union/Mistake

Source Work

1964: Murray R. Spiegel: Theory and Problems of Complex Variables

Chapter $1$: Complex Numbers

Supplementary Problems: $123 \ \text{(c)}$

This mistake can be seen in the 1981 printing of the second edition (1974) as published by Schaum: ISBN 0-070-84382-1

Mistake

If $A$, $B$ and $C$ are the point sets defined by $\cmod {z + i} < 3$, $\cmod z < 5$, $\cmod {z + 1} < 4$, represent graphically each of the following:

$\textit {(a)} \quad A \cap B \cap C$, $\quad \textit {(b)} \quad A \cup B \cup C$, $\quad \textit {(c)} \quad A \cap B \cup C$, $\quad \textit {(d)} \quad C \paren {A + B}$, $\quad \textit {(d)} \quad \paren {A \cup B} \cap \paren {B \cup C}$, $\quad \textit {(e)} \quad AB + BC + CA$, $\quad \textit {(f)} \quad A \tilde B + B \tilde C + C \tilde A$

Correction

It's a minor point, but shows lack of attention to detail:

The exercises are lettered: $\text {(a)}$, $\text {(b)}$, $\text {(c)}$, $\text {(d)}$, $\text {(d)}$, $\text {(e)}$, $\text {(f)}$

To wit: two instances of $\text {(d)}$.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Point Sets: $123$