Discrete 2.2 Set Operations

Union of sets A and B, denoted A∪B

The set containing the elements in A or B (or both)

A ∪ B = {x | x ∈ A ∨ x ∈ B}

Intersection of sets A and B, denoted A∩B

The set containing the elements in both A and B. If two sets have an empty intersection, they are disjoint.

A ∩ B = {x | x ∈ A ∧ x ∈ B}

Difference of sets A and B, denoted A-B

The set containing the elements of A that are not also in B.
A − B = {x | x ∈ A ∧ x ∉ B}

Complement of set A, denoted Ā

The set containing the elements (in U) that are not in A
Ā= {x ∈ U | x ∉ A}

{x | x ∈ A_j, for some j ∈ {1, 2, 3, ..., n}}

{x | x∈A_j, for all j∈{1, 2, 3, ..., n}}

{x | x∈A_j, for some j∈ℤ⁺}

{x | x∈A_j, for all j∈ℤ⁺}