A binary relation \( R \) is a, when \( \left ( x , y \right ) \in R \), then we write \( x R y \) to say that \( x \) is related to \( y \).
Note: A binary relation on \( X \times X \) is stated simply as a relation on \( X \)
An equivalence relation is a, and relation
when \( R \) is an equivalence relation, we denote it by \( ~ \) instead of \( R \)
Given any \( a \in G \), then clearly \( a \% n = a \% n \) so that \( a R a \), if \( a R b \), then \( a \% n = b \% n \) and then \( b \% n = a \% n \), finally if \( a \% n = b \% n \) and \( b \% n = c \% n \) therefore \( a \% n = c \% n \)
a partial order is a binary relation \( R \) on a set \( X \) such that for any \( a , b , c \in X \) we have that:
Note that the above three statements equivalently say that \( \le \) is a reflexive, anti-symmetric and transitive relation.