Set Theory/Examples/Unions and Intersections 2

Examples in Set Theory

Let:

$\ds A$

$=$

$\ds \set {1, 2}$

$\ds B$

$=$

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

$\ds C$

$=$

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

$\ds D$

$=$

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

Then:

$\ds A \cap B$

$=$

$\ds \set 1$

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

$=$

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

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

$=$

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

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

$=$

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

1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 2$. Sets of sets: Exercise $1$