16. Relations
The chapter focuses on the concept of relations within the context of mathematics, exploring their definitions, properties, and representations. It emphasizes binary relations as the primary focus while also discussing special types of relations and their characteristics. Additionally, various methods for representing these relations, such as matrix and graph representations, are highlighted.
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What we have learnt
- A relation is defined as a subset of the Cartesian product of two sets.
- Binary relations can be represented in multiple ways, including using matrices and directed graphs.
- Reflexive relations relate every element of a set to itself, and this condition must hold true for all elements for a relation to be classified as reflexive.
Key Concepts
- -- Relation
- A relation is a subset of the Cartesian product of two sets where certain pairs satisfy a relationship.
- -- Binary Relation
- A binary relation is a relation that connects elements from two sets, A and B, represented as subsets of A x B.
- -- Matrix Representation
- A relation can be represented as a Boolean matrix that indicates the presence or absence of relationships between elements of the two sets.
- -- Directed Graph
- A graphical representation of a relation where vertices represent elements of the sets and directed edges indicate relationships.
- -- Reflexive Relation
- A reflexive relation is one where every element in the set is related to itself, meaning all diagonal entries in the matrix representation are 1.
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