Set Intersection/Examples/4 Arbitrarily Chosen Sets of Complex Numbers

Example of Set Intersection

Let:

$\ds A$

$=$

$\ds \set {1, i, -i}$

$\ds B$

$=$

$\ds \set {2, 1, -i}$

$\ds C$

$=$

$\ds \set {i, -1, 1 + i}$

$\ds D$

$=$

$\ds \set {0, -i, 1}$

Then:

$\paren {A \cup C} \cap \paren {B \cup D} = \set {1, -i}$

$\ds \paren {A \cup C} \cap \paren {B \cup D}$

$=$

$\ds \paren {\set {1, i, -i} \cup \set {i, -1, 1 + i} } \cap \paren {\set {2, 1, -i} \cup \set {0, -i, 1} }$

$\ds $

$=$

$\ds \set {1, i, -i, -1, 1 + i} \cap \set {2, 1, -i, 0}$

Definition of Set Union

$\ds $

$=$

$\ds \set {1, -i}$

$\blacksquare$

1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Point Sets: $121 \ \text{(c)}$