# 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:

 $\ds A \cap B$ $=$ $\ds \set 1$ $\ds \paren {B \cap D} \cup A$ $=$ $\ds \set {1, 2, \set 2}$ $\ds \paren {A \cap B} \cup D$ $=$ $\ds \set {1, \set 1, \set 2, \set {1, 2} }$ $\ds \paren {A \cap B} \cup \paren {C \cap D}$ $=$ $\ds \set {1, \set 1, \set 2}$