🎯 Learning Objectives

By the end of this lesson, you should be able to:

• Define what a set is and use correct set notation.
• List the elements of a given set.
• Understand and find the Union (∪) and Intersection (∩) of sets.
• Represent simple sets using Venn diagrams.

1. What is a Set?

A set is a well-defined collection of distinct objects. These objects are called elements or members of the set.

• Sets are usually named with capital letters (e.g., Set A, Set B).
• Elements are listed inside curly brackets { } and separated by commas.
• Example: If A is the set of the first three natural numbers, we write: A = {1, 2, 3}

2. Special Sets and Symbols

• ∈ (Element of): Means "belongs to". If A = {1, 2, 3}, then 1 ∈ A (1 is an element of A).
• ∉ (Not an element of): Means "does not belong to". 4 ∉ A.
• n(A): Represents the number of elements in set A. If A = {1, 2, 3}, then n(A) = 3.
• ∅ or { }: The Empty Set (or Null Set). A set with no elements.

3. Set Operations

Just like we add and subtract numbers, we can combine sets.

A. Union of Sets ( ∪ )

The union of two sets, written as A ∪ B, is a new set containing all the elements that are in A, in B, or in both. (Think: "Combine them, but don't write duplicates").

Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.

B. Intersection of Sets ( ∩ )

The intersection of two sets, written as A ∩ B, is a new set containing only the elements that are common to both A and B. (Think: "What do they share?").

Example: If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.

4. Venn Diagrams

A Venn diagram uses circles to visually represent sets and their relationships.

• The rectangle represents the Universal Set (everything we are considering).
• Each circle represents a set.
• The overlapping area of two circles represents the Intersection (A ∩ B).
• The entire area covered by both circles represents the Union (A ∪ B).

📌 Summary

Sets help us organize and categorize information logically. Remember: Union (∪) means "OR" (combine everything), and Intersection (∩) means "AND" (only the shared parts).