Condition for Composite Relation with Inverse to be Identity/Examples

Examples of Use of Condition for Composite Relation with Inverse to be Identity

Arbitrary Example $1$

In the above we see that:

$\RR$ is many-to-one

$\RR$ is right-total

$\RR \circ \RR^{-1} = I_T$.

Note, however, that $\RR^{-1}$ is neither many-to-one nor right-total, and does not need to be for $\RR \circ \RR^{-1} = I_T$.