Overview

This topic introduces the language of sets and how to perform operations involving union, intersection, complements, and subsets. You'll learn how to use Venn diagrams to represent relationships, identify disjoint and overlapping sets, and solve problems involving set membership and classification.

Key Concepts and Structures

• Set: A collection of distinct elements. Example: A = {1, 2, 3}
• Element: A member of a set. Written as x ∈ A
• Subset: All elements of set A are also in B: A ⊆ B
• Proper Subset: A ⊂ B and A ≠ B
• Union: Elements in either set: A ∪ B
• Intersection: Elements in both sets: A ∩ B
• Complement: Elements not in the set: A' or U - A (relative to universal set)
• Disjoint Sets: No elements in common. A ∩ B = ∅
• Equal Sets: Every element is shared between both: A = B
• Venn Diagrams: Visual tool to represent sets and their relationships

Step-by-Step Example

Problem: Given A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find:

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

Step 2: Intersection:
A ∩ B = {3, 4}

Step 3: Complement (assuming universal set U = {1–6}):
A' = {5, 6}

Final Answer:
A ∪ B = {1, 2, 3, 4, 5, 6}
A ∩ B = {3, 4}
A' = {5, 6}

Quick Tip