Example of Set Intersection with Union/Mistake

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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


If $A$, $B$ and $C$ are the point sets defined by $\cmod {z + i} < 3$, $\cmod z < 5$, $\cmod {z + 1} < 4$, represent graphically ... :
$\textit {(c)} \quad A \cap B \cup C$


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.