Set relations

reflexive

reflexive if, for every element \(a \in A\) we have \(aRa \Rightarrow (a, a) \in R\)

• \( A = \{(a, a): a \in A\}\)

Symmetric

symmetric iff \((x,y) \in R \wedge (y,x) \in R\)

Transitive

Iff R relates \(a\) to \(b\) and \(b\) to \( c\) then \(a \) relates to \(c\)

• \(a < b < c \rightarrow a < c\)
• \(a = b = c \rightarrow a = c\)