# Example of Set Intersection with Union/Mistake

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## Contents

## 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 ... :*

- $\textit {(c)} \quad A \cap B \cup C$

## Correction

Without any definition of binding priority between set intersection and set union, $A \cap B \cup C$ is ambiguous.

It can mean either:

- $(1): \quad A \cap \paren {B \cup C}$

which can be represented graphically as follows:

or as:

- $(2): \quad \paren {A \cap B} \cup C$

which can be represented graphically as follows:

As can be seen, the two are not the same.

## Sources

- 1981: Murray R. Spiegel:
*Theory and Problems of Complex Variables*(SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Point Sets: $123 \ \text{(c)}$