Day 01 – Discrete mathematics for computer science set operation Union Intersection.

Day 01 – Discrete mathematics for computer science set operation Union Intersection.

 Discrete Mathematics for Computer Science – Set Operations (Union & Intersection)

 Topic: Set Operations – Union & Intersection
 Subject: Discrete Mathematics
 Useful For: CSE / IT / GATE / Competitive Exams

 What is a Set?

A set is a collection of distinct elements. It is usually represented using curly brackets {}.

Example:
Set A = {1, 2, 3, 4}
Set B = {3, 4, 5, 6}

 Union of Sets (A ∪ B)

The Union (A ∪ B) of two sets includes all elements from both sets, without repetition.

Formula:

$$A\cup B=\{x|x\in A\text{ or }x\in B\}$$

(Union takes all elements from A and B.)

Example:
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
A ∪ B = {1, 2, 3, 4, 5, 6}

Key Points:
Union combines elements from both sets.
Duplicates are removed.

 Intersection of Sets (A ∩ B)

The Intersection (A ∩ B) of two sets includes only the common elements present in both sets.

Formula:

$$A\cap B=\{x|x\in A\text{ and }x\in B\}$$

(Intersection finds common elements in A and B.)

Example:
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
A ∩ B = {3, 4}

Key Points:
Intersection only includes elements that exist in both sets.
If no common elements, intersection = Ø (empty set).

 Venn Diagram Representation

Union (A ∪ B) – Covers all elements in both sets.
Intersection (A ∩ B) – Covers only the overlapping region of both sets.

Venn Diagram for A ∪ B and A ∩ B:

Union (A ∪ B)
(Everything inside both circles is included)

Intersection (A ∩ B)
(Only overlapping part of both circles is included)

 Properties of Union & Intersection

 Applications of Set Operations in Computer Science

 Database Management (SQL Queries) 

UNION operation in SQL retrieves all records from two tables.
INTERSECTION retrieves common records from two tables.

 Artificial Intelligence & Machine Learning 

 Used in classification algorithms to find common or unique data points.
Feature selection in AI models.

 Networking & Cybersecurity 

 Firewalls use set operations to filter allowed & blocked IPs.
Set-based filtering in packet transmission.

 Searching Algorithms & Data Structures 

 Used in hashing & indexing for fast lookup.
Set operations optimize search results.

 Probability & Statistics 

 Probability uses Union & Intersection to calculate event occurrences.

 Summary

Union (A ∪ B) → All elements from both sets (Duplicates removed).
Intersection (A ∩ B) → Common elements in both sets.
Used in Databases, AI, Networking, and Algorithms.

Would you like more examples, a Venn diagram, or explanations in Hindi?

Day 01 – Discrete mathematics for computer science set operation Union Intersection.

DISCRETE MATHEMATICS FOR COMPUTER SCIENCE