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Sets

Elementary

Definition

A set is a collection of distinct, well-defined objects. It's one of the most fundamental concepts in mathematics.

A ∪ B = x : x ∈ A or x ∈ B

Union

A ∩ B = x : x ∈ A and x ∈ B

Intersection

A - B = x : x ∈ A and x ∉ B

Difference

|A ∪ B| = |A| + |B| - |A ∩ B|

Inclusion-exclusion principle

Example 1

If A = {1, 2, 3} and B = {2, 3, 4}, find A ∪ B and A ∩ B.

Discovered by: Georg Cantor (1874)

Cantor founded set theory while studying how to compare sizes of infinite sets.

SQL UNION, INTERSECT operations

Set data structure

Truth sets of propositions