Summary  
This chapter covers defining and manipulating set data structures in Python, including union, intersection, difference, symmetric difference, subset/superset checks, and using sets to remove duplicate elements.

General domain of usage  
Data science

## Breaking Down the Python Code

### Defining Sets
A **set** is defined using curly brackets `{}` or the `set()` function. Sets **do not allow duplicate values** and do not maintain any specific order.

# Define two sets
set_a = {1, 2, 3, 4, 5}
set_b = set([4, 5, 6, 7, 8])

print("Set A:", set_a)
print("Set B:", set_b)

Even if we define a set with duplicate values, Python **automatically removes** the duplicates.

### Union of Sets
Combines elements from **both sets**. **No duplicates** are included.


set_a = {1, 2, 3, 4, 5}
set_b = {4, 5, 6, 7, 8}

union_set = set_a.union(set_b)
print("Union:", union_set)

### Intersection of Sets

Returns only the elements **common to both sets**.


set_a = {1, 2, 3, 4, 5}
set_b = {4, 5, 6, 7, 8}

intersection_set = set_a.intersection(set_b)
print("Intersection:", intersection_set)

### Difference of Sets
Finds elements in `set_a` that are **NOT** in `set_b`.


set_a = {1, 2, 3, 4, 5}
set_b = {4, 5, 6, 7, 8}

difference_set = set_a.difference(set_b)
print("Difference (A - B):", difference_set)

### Symmetric Difference
Finds elements that are in **either set**, but **NOT in both**.


set_a = {1, 2, 3, 4, 5}
set_b = {4, 5, 6, 7, 8}

symmetric_difference_set = set_a.symmetric_difference(set_b)
print("Symmetric Difference:", symmetric_difference_set)

### Subset and Superset Relationships
- `issubset()` checks if **all elements of one set exist in another**;
- `issuperset()` checks if **one set fully contains another**.


set_a = {1, 2, 3, 4, 5}
set_b = {4, 5, 6, 7, 8}

print("Is A a subset of B?", set_a.issubset(set_b))
print("Is A a superset of {3, 4}?", set_a.issuperset({3, 4}))

### Removing Duplicates Using Sets
A common **real-world use case** for sets is removing duplicates from a list.


data = [1, 2, 2, 3, 4, 4, 5]
unique_data = set(data)
print("Unique values:", unique_data)

Since sets **do not allow duplicates**, converting a list into a set automatically removes repeated values.

Master the mathematical foundations essential for data science. Explore core concepts in functions, calculus, linear algebra, probability, and dimensionality reduction. Build both theoretical understanding and practical coding experience to strengthen your ability to analyze data, model complex systems, and apply advanced techniques in machine learning.

Explore the foundation of mathematical functions. Learn different types of algebraic and transcendental functions, their properties, and how to implement them in Python to solve real-world problems.

Master the concepts of sets and series, from basic operations to practical applications. Gain hands-on experience implementing set operations and working with arithmetic and geometric series in Python.

Develop a solid understanding of limits, derivatives, integrals, and partial derivatives. Connect theory to practice by implementing these concepts in Python and applying them to optimization through gradient descent.

Build strong knowledge of vectors, matrices, and transformations. Learn decomposition methods and eigenvalue analysis, while reinforcing concepts with Python coding challenges and practical data science applications.

Dive into probability theory and statistics. Study conditional probability, Bayes' theorem, and statistical measures. Implement key concepts in Python, simulate distributions, and strengthen your skills through challenges and quizzes.

Implementing Sets in Python

Breaking Down the Python Code

Defining Sets

Union of Sets

Intersection of Sets

Difference of Sets

Symmetric Difference

Subset and Superset Relationships

Removing Duplicates Using Sets