Union Distributes over Intersection/Examples

Examples of Use of Union Distributes over Intersection

Let:

\(\ds A\)

\(=\)

\(\ds \set {2, 4, 6, 8, \dotsc}\)

\(\ds B\)

\(=\)

\(\ds \set {1, 3, 5, 7, \dotsc}\)

\(\ds C\)

\(=\)

\(\ds \set {1, 2, 3, 4}\)

Then:

Arbitrary Integer Sets: $1$

$A \cup \paren {B \cap C} = \set {1, 2, 3, 4, 6, 8, \dotsc} = \paren {A \cup B} \cap \paren {A \cup C}$

Arbitrary Integer Sets: $2$

$B \cup \paren {A \cap C} = \set {1, 2, 3, 4, 5, 7, \dotsc} = \paren {B \cup A} \cap \paren {B \cup C}$