Set Operations: Intersection and Union

Set Theory Basics

• The cardinality of the set {2, 4, 6, 8} is 4.
• The symbol "∈" is used to denote "is an element of" in set theory.
• The statement "-5 is an element of the set {5, 10, 15, 20, 25}" is False.
• The cardinal number of a set is represented by the notation "| |" or "card()".

Set Builder Notation

• The expression {x | x is an even counting number less than 10} means the set of all even counting numbers less than 10.

Set Operations

• The symbol "∉" is used to denote "is not an element of" in set theory.
• The intersection of sets {1, 3, 5} and {2, 4, 6} is the empty set, ∅.
• The union of sets {1, 3, 5} and {3, 4, 5} is the set {1, 3, 4, 5}.
• (A ∪ B) ∩ C = ∅, given A = {m, n}, B = {n, o}, and C = {a, b}.
• The symmetric difference between sets {1, 2, 3} and {2, 3, 4} is the set {1, 4}.
• (A ∪ B) - (B ∩ C) = {p, r}, given A = {p, q}, B = {q, r}, and C = {p, r}.
• The complement of (A ∪ B) is {3, 4}, given U = {1, 2, 3, 4}, A = {1, 2}, and B = {2, 3}.
• The symmetric difference, A ∆ B, is defined as (A ∪ B) - (A ∩ B).

Venn Diagrams

• Shading in Venn Diagrams represents regions of the sets.
• U – (A ∩ B) is equal to the region of U not in the intersection of A and B.
• (A′ ∩ B′) ∩ C on a Venn diagram represents the region of C that is not in A and not in B.
• A – B is equivalent to A ∩ B′.