Example of Set Intersection with Union/Mistake
Jump to navigation
Jump to search
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: $123 \ \text{(c)}$