# Transitive Property

Definition : Let R be a relation, R is transitive if, for any a, b and c in G, then aRb and bRc implies aRc.

A quick example is R defined as $a > b$. Now if $a >b$ and $b>c$ then $a>c$. Here’s another example, Let R be defined as $\mod 5$. $1 \mod 5 \equiv 6 \mod 5$ and $6 \mod 5 \equiv 11\mod 5$ this means that $1 \mod 5 \equiv 11 \mod 5$ since both $1$ and $11$ both have a remainder of $1$ when divided by $5$.