One of the most important operations is set intersection. Mathematically, you need to use the ∩ symbol to represent this intersection operation.

Properties | Value |
---|---|

Symbol | Union |

Argument | No |

Command | `\cap` |

Example | `\cap` → ∩ |

As you may know, the `\cup`

command is used to represent union symbols using latex. In the same way, you need to use `\cap`

command to represent intersection symbol.

```
\documentclass{article}
\begin{document}
\[ s_{1} \cap s_{2} \]
\end{document}
```

**Output :**

You may have noticed that the big intersection symbol is used in many science documents.

```
\documentclass{article}
\begin{document}
\[ s_{1} \bigcap s_{2} \]
\end{document}
```

**Output :**

In Latex, the default `\bigcap`

command is used to denote this Big Union symbol.

## Latex intersection symbol with latex

When the intersection operation is performed in the n number set. In that case, limits are used above and below the big intersection symbol as a sum.

```
\documentclass{article}
\begin{document}
\[ \bigcap\limits_{i=1}^{n}F_{i} \]
\[ \bigcap_{i=1}^{n}A_{i} \]
\end{document}
```

**Output :**

If you use big intersection symbol in the text, that is inline, then the shape of symbol can be changed.

```
\documentclass{article}
\begin{document}
latex eqn $\bigcap_{i=1}^{n}x_{i}$
\end{document}
```

**Output :**

If you perform an intersection operation within the disjoint set, it will return an empty set. The `\emptyset`

command is used for this Empty set in Latex.

```
\documentclass{article}
\begin{document}
\[ s_{1}\cap s_{2}=\emptyset \]
\end{document}
```

**Output :**

Many times intersection operations are performed on infinity number sets. In that case, the upper limit would be infinity.

```
\documentclass{article}
\begin{document}
\[ \bigcap_{i=1}^{\infty}A_{i} \]
\end{document}
```

**Output :**

You do not need to install any external packages in Latex for all the symbols used above.