TeXipedia

cup

Represents the union operation between sets in mathematical notation, combining elements from multiple sets into a single set.

Overview

Essential in set theory and mathematical logic for describing the combination of sets where elements from either set are included in the result.

  • Commonly used in discrete mathematics and computer science for describing database operations
  • Appears frequently in probability theory when working with event spaces
  • Forms a fundamental part of algebraic set operations alongside intersection and complement
  • Often paired with its counterpart intersection (\cap) in mathematical proofs and set theory exercises

Examples

Set union operation between two sets A and B.

A∪B={x:x∈A or x∈B}A \cup B = \{x : x \in A \text{ or } x \in B\} 
A \cup B = \{x : x \in A \text{ or } x \in B\}

Union of multiple sets in an indexed family.

⋃i=1nAi=A1∪A2∪⋯∪An\bigcup_{i=1}^{n} A_i = A_1 \cup A_2 \cup \cdots \cup A_n 
\bigcup_{i=1}^{n} A_i = A_1 \cup A_2 \cup \cdots \cup A_n

Set theory expression showing union of probability events.

P(E1∪E2)=P(E1)+P(E2)−P(E1∩E2)P(E_1 \cup E_2) = P(E_1) + P(E_2) - P(E_1 \cap E_2) 
P(E_1 \cup E_2) = P(E_1) + P(E_2) - P(E_1 \cap E_2)