If you need to find all unique elements from the list or find common or uncommon elements from two or more lists, **Python sets** are what you’re looking for. In this article, we’ll cover Python sets in detail and show how to get results of mathematical operations like union, intersection, symmetric difference, etc.

## Table of contents

## What is Python set?

A Python set is a collection of **unordered**, **unindexed,** and **unchangeable** items where all **elements are unique** (no duplicated elements).

There are two classes of sets that are available for you:

- set – this is a
**mutable**collection of elements, so you can add or remove items in set when needed - frozenset – this is immutable collection of elements, so you can’t change the set as soon as you’ve created it

To answer those questions, sets allow us to use mathematical set operations like union, intersection, symmetric difference, etc., which we’ll cover down below.

## Advantages of Python sets

Python sets cannot store duplicate elements within them, so Python sets are highly useful for:

- Efficient removal of duplicate elements from a list and tuples
- Applying common mathematical operations like unions, intersections, differences, and asymmetric differences to collections of elements.

## Sets vs lists and tuples

Here are two major differences between sets, lists, and tuples in Python:

- Lists and tuples store values in a sequence and can have duplicates.
- Sets store unordered values and can not have duplicates.

## Managing Python sets

In this section, we’ll cover the basic operations with sets.

### Creating Python set

You can create a set by putting all the set elements separated by commas inside curly braces `{}`

, or by using `set()`

class.

A set may consist of any number of elements of different types (integer, float, tuple, string, etc.), but it cannot contain mutable elements like lists, sets, dictionaries, or classes.

Here’s how you’re defining a set:

```
# elements of the same type
set_example = {3, 1, 2}
print(f'Example 1: {set_example}')
# elements of mixed type
set_example = {5.5, (1, 1, 0), "Joe"}
print(f'Example 2: {set_example}')
# set can't store duplicates
set_example = {1, 2, 3, 4, 3, 2}
print(f'Example 3: {set_example}')
```

If you’d like to initialize an **empty set**, you can not use {}, because such syntax will create an empty dictionary.

Instead, use the set() class directly:

```
set_example = set()
print(set_example)
```

An attempt to store mutable elements in a set

`set_example = {[1, 2], 3}`

will throw an exception:

```
Traceback (most recent call last):
File "", line 1, in
TypeError: unhashable type: 'list'
```

### Accessing elements in Python set

You can not access set items by referring to their index values, since sets do not have an index.

Instead, you can:

- Loop through the set items using a for loop
- Check if a specified value is present in a set, by using the in keyword

Here’s an example:

```
set_example = set(["hands", "on", "cloud"])
print(f'Example set: {set_example}')
# Accessing elements using
# for loop
for element in set_example:
print(f'Elements of set: {element}')
# Check if element exists in set
element = "cloud"
if element in set_example:
print(f'Element "{element}" exists in set')
```

### Adding elements to Python set

There are two methods available for you in the set class to add elements to the Python set:

`add(element)`

– adds one element at a time`update([elements_list])`

– adds two or more elements to a set at a time from the list

**Note**: element of the type list cannot be used in the `add()`

method because the list is a mutable data type in Python.

Here’s an example:

```
set_example = set()
print(f'Initial set state: {set_example}')
# Adding elements to the set
set_example.add("hands")
set_example.add("on")
set_example.add("cloud")
set_example.add("313377")
print(f'Set state after adding elements: {set_example}')
# updating elements
set_example.update(["hands", True])
print(f'Set state after updating elements: {set_example}')
```

### Removing elements from Python set

There are four methods available for you in the set class to remove elements to the Python set:

`remove(element)`

– removes element from the set or raises KeyError exception if the element does not exist`discard(element)`

– deletes element from the set (the set ramains unchanged if there’s no such element in it)`clear()`

– removes all the elements from the set`pop()`

– removes last element from the set

```
set_example = set([1, 2, 3, 4, 5, 6, 7, 8, 9, 0])
print(f'Initial set state: {set_example}')
set_example.remove(1)
print(f'Set state after remove(): {set_example}')
set_example.discard(1)
set_example.discard(2)
print(f'Set state after discard(): {set_example}')
set_example.pop()
print(f'Set state after pop(): {set_example}')
set_example.clear()
print(f'Set state after clear(): {set_example}')
```

## Iterating over sets in Python

There’s no way to access individual elements within a set by index, instead, you can iterate over set elements:

```
set_1 = {1, 2, 3, 4, 5}
for element in set_1:
print(f'Set element: {element}')
```

## Test element membership in a set

You can check if an item exists in a set by using the `in`

keyword:

```
set_1 = {1, 2, 3, 4, 5}
element = "hands-on.cloud"
if element in set_1:
print(f'"{element}" belongs to the set {set_1}')
else:
print(f'"{element}" does not belong to the set {set_1}')
```

## Ordering set values

If you need to get the values from the set in order, you can use the `sorted`

function to get an ordered list of set elements:

```
set_1 = {"x", "a", "g", "y", "t"}
ordered_list = sorted(set_1)
print(f'Set "{set_1}" elements in ordered form: {ordered_list}')
```

## Remove duplicates from list

Sets are the fastest way to remove duplicates from a list. Let’s take a look, how to do it:

```
list_with_dups = ["x", "a", "a", "t", "t"]
list_without_dups = list(set(list_with_dups))
print(f'{list_with_dups} => {list_without_dups}')
```

## Set operations in Python

In this part of the article, we’ll review the fundamental operations through which sets can be combined and related to each other.

### Union

The union operation on two sets produces a new set that contains all elements from both sets.

Here’s a code example:

```
set_1 = {1, 2, 3, 4, 5}
set_2 = {4, 5, 6, 7, 8}
result_set = set_1 | set_2
print(f'Result set: {result_set}')
```

### Intersection

The intersection operation on two sets produces a new set containing only common elements from both sets.

Here’s a code example:

```
set_1 = {1, 2, 3, 4, 5}
set_2 = {4, 5, 6, 7, 8}
result_set = set_1 & set_2
print(f'Result set: {result_set}')
```

### Difference

The difference operation between two sets produces a new set containing only the elements from the first set and none from the second set.

Here’s a code example:

```
set_1 = {1, 2, 3, 4, 5}
set_2 = {4, 5, 6, 7, 8}
result_set = set_1 - set_2
print(f'Result set: {result_set}')
```

### Symmetric difference

The symmetric difference operation between two sets produces a new set containing only the elements that belong to both sets at the same time.

Here’s a code example:

```
set_1 = {1, 2, 3, 4, 5}
set_2 = {4, 5, 6, 7, 8}
result_set = set_1 ^ set_2
print(f'Result set: {result_set}')
```

### Comparing sets

You can check if one set is a subset or superset of another set. The result of the comparison operation is `True`

or `False`

:

```
set_1 = {1, 2, 3, 4, 5}
set_2 = {4, 5}
if set_2 <= set_1:
print(f'Set {set_1} is superset for set {set_2}')
if not set_2 >= set_1:
print(f'Set {set_1} is NOT superset for set {set_2}')
```

## Frozenset in Python

The **frozenset** is a new class in Python that has the characteristics of a regular set, but its elements cannot be changed once frozenset has been initialized. In the same way, as tuples are immutable lists, frozensets are immutable sets. So, frozensets are useful in situations where you need to use a set, but a set itself should be immutable.

Frozensets are hashable and can be used as keys to dictionaries.

You can create a frozenset using the frozenset() class constructor:

```
set_1 = frozenset([1, 2, 3, 4, 5])
set_2 = frozenset([4, 5, 6, 7, 8])
```

Frozensets supports the same operations as regular sets:

```
# Union
result_set = set_1 | set_2
print(f'Result set: {result_set}')
# Intersection
result_set = set_1 & set_2
print(f'Result set: {result_set}')
# Difference
result_set = set_1 - set_2
print(f'Result set: {result_set}')
# Symmetric difference
result_set = set_1 ^ set_2
print(f'Result set: {result_set}')
```

## Summary

In this article, we’ve covered Python `sets`

, `frozensets`

and how to use them to get results of collections union, intersection, symmetric difference, etc.