Union & Intersection

Venn Diagram

use to show relationships between items

 

Set Operations (Union & Intersection)

$A \cup B = \{x\ |\ x \in A\ or\ x \in B\}$ : Union

$A \cap B = \{x\ |\ x \in A\ and\ x \in B\}$ : Intersection

$e.g.\ A = \{1, 2, 3, 4\},\ B = \{3, 4, 5, 6\},\ then,\ A \cup B = \{1, 2, 3, 4, 5, 6\},\ A \cap B = \{3, 4\}$

 

 

Properties of Union and Intersection

$A \cup B = B \cup A,\ A \cap B = B \cap A$ : Commutative Law

$(A \cup B) \cup C = A \cup (B \cup C),\ (A \cap B) \cap C = A \cap (B \cap C)$ : Associative Law

$A \cup (B \cap C) = (A \cup B) \cap (A \cup C),\ A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$ : Distributive Law

$A \cup \{ \} = A,\ A \cap \{ \} = \{ \}$

$A \cup U = U$

$A \cup A = A, A \cap A = A$ : Idempotent Law