An important concept in set operation is union operation. Union symbols are used for this union operation. And this union symbol is marked by ∪.
| Properties | Value |
|---|---|
| Symbol | Union |
| Argument | No |
| Command | \cup |
| Example | \cup → ∪ |
With the help of latex, you need to use \cup command to represent union symbols in a scientific document. So, look at this example below
\documentclass{article}
\begin{document}
\[ A \cup B = \{x : x\in A \; or \; x\in B \} \]
\[ A \cup \phi \; or \; A\cup \{\} = A \]
\[ (A_1 \cup A_2 \cup A_3 \cup \cdots A_n)^c=A_1^c \cap A_2^c \cap A_3^c\cdots \cap A_n^c \]
\[ A\cup (B\cup C)=(A\cup B)\cup C \]
\end{document}Output :
Big union symbol in LaTeX
When a union is defined between more than three sets, it is represented in the form of n summation. However, the only difference is that union symbol is used instead of summation symbol.
\documentclass{article}
\begin{document}
\[ \cup_{i=1}^{n}F_{i} \]
\end{document}Output :
If you look at the output above, you will see ,the lower limit and upper limit are not located above and below in union symbol. Thus, the above latex union symbol is not the best practice for union operations of n number sets.
For this you need to use Big Union symbol. And you have to use limits above and below this Big Union symbol. So, look at this program below
\documentclass{article}
\begin{document}
\[ \bigcup_{i=1}^{n}F_{i} \]
\end{document}Output :
In latex, you need to use \bigcup command for big union symbol. And there is no need to install any external package in latex for this command.
You can add upper and lower limits using \limits command with Big Union.
\documentclass{article}
\begin{document}
\[ \bigcup\limits_{i=1}^{n}F_{i} \]
\end{document}Output :
In the case of n number sets, in my opinion, the last two methods are best practice.
LaTeX disjoint union symbol
Generally, disjoint union symbols in latex are characterized by the following three methods.
1. You can represent a disjoint union symbol in a document by using a dot symbol over the union symbol. For this you need to use \dot\cup command.
\documentclass{article}
\begin{document}
\[ S_{1} \dot\cup S_{2} \]
\end{document}Output :
2. Second, you can use \uplus command. And this will add a plus symbol to union symbol and return the output to you.
\documentclass{article}
\begin{document}
\[ S_{1} \uplus S_{2} \]
\end{document}Output :
3. Third, you can use four corner u shape symbols.
\documentclass{article}
\begin{document}
\[ S_{1} \sqcup S_{2} \]
\end{document}Output :
You can use disjoint union symbol document by installing an external latex package without using above three default methods.
