Relations between two sets | Definition + First Examples

About this Video

• Video Title: Relations between two sets | Definition + First Examples
• Channel: Dr. Trefor Bazett
• Speakers: Dr. Trefor Bazett
• Duration: 00:06:39

Introduction

This video introduces the concept of relations between two sets in mathematics. Dr. Bazett explains the definition of a relation using examples, including comparing integers using the "less than" symbol and illustrating a relation between sets of humans and their pets (ownership). The video culminates in a formal definition of a relation as a subset of the Cartesian product of two sets.

Key Takeaways

• Relations compare or relate objects: Mathematics often involves relating one item to another, establishing a comparison or relationship.
• Ordered pairs and relationships: Relationships between elements of two sets are represented as ordered pairs. The order matters; (2,5) is different from (5,2).
• Relations as subsets: A relation between sets A and B is formally defined as a subset of the Cartesian product (A x B). This means it's a collection of ordered pairs (a,b) where 'a' belongs to A and 'b' belongs to B. Not all possible pairings need to be part of the relationship.