How to write a union symbol(∪) in LaTeX?

In set theory, the union of sets is a fundamental operation, represented by the symbol ∪. It denotes the combination of elements from two or more sets.

To include this symbol in a scientific document using LaTeX, use the \cup command. Below is an example demonstrating its usage.

\[ A \cup B = \{x : x\in A \; or \; x\in B \} \]
  \[ A \cup \phi \; or \; A\cup \{\} = A \]
  \[ (A_1 \cup A_2 \cup A_3 \cup \cdots A_n)^c=A_1^c \cap A_2^c \cap A_3^c\cdots \cap A_n^c \]
  \[ A\cup (B\cup C)=(A\cup B)\cup C \]

Output :

A1 ∪ A2

Big union symbol

When working with multiple sets, the union notation resembles summation notation but uses instead of . In LaTeX, you can write.

\[ \cup_{i=1}^{n}F_{i} \]

Output :

Mathematical notation for multiple sets using ∪

However, this does not properly position the limits. To correctly display them, use the \bigcup command.

\[ \bigcup_{i=1}^{n}F_{i} \]

Output :

Properly formatted notation using big ∪

To correctly position upper and lower limits, use \limits with \bigcup. More details are provided below

\[ \bigcup\limits_{i=1}^{n}F_{i} \]

Output :

Properly formatted ∪ symbol using \limits command

Among these options, the last two methods are the most effective for handling unions over multiple sets.

Disjoint union symbol

In LaTeX, there are three primary ways to represent a disjoint union operation in a document.

Using a Dot Over the Symbol

One method is to place a dot above the symbol. This can be done using the \dot{\cup} command.

\[ S_{1} \dot\cup S_{2} \]

Output :

Mathematical notation with a dot over the symbol

Using a Plus Sign

Another method is to use the \uplus command, which adds a small plus sign to the symbol, providing a distinct visual representation.

\[ S_{1} \uplus S_{2} \]

Output :

Notation for U plus sign

Four-corner U-shaped

Alternatively, you can use a four-corner U-shaped symbol with the \sqcup command.

\[ S_{1} \sqcup S_{2} \]

Output :

Mathematical notation with U-shaped symbols

In addition to these default methods, you can also install an external LaTeX package to access more advanced notations.

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