2.3 Relation

#Type/Definition #Topic/Linear_Algebra

Types: 2.5 Function (Set Theory)
Examples: 2.3.1 Traffic Light Relation, 2.3.2 Dial Pad Relation
Constructions: N/A
Generalizations: N/A

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Relation

Let $A$ and $B$ be sets. The set $R$ is a relation from $A$ to $B$ iff

R \subseteq A \times B .

A relation from $A$ to itself is called a relation on $A$ .
If $(a, b) \in R$ , we write $a R b$ and say that $a$ is related to $b$ .
If $(a, b) \notin R$ , then $a R b$ .