We define the following operations on relations: Composition: For:

$$T: A$$B

$$S: B$$C

We define the composition as:

T $$ S $=\{($a$,$ c$)|($b in B$)($aT b $$ bSc$)\}$

Transposed Relation: R$^$T If R: A$$B$,$R$^$T: B$$A and R$^$T$=\{($b$,$a$)|($a$,$b$)$ in R$\}$

Prove or disprove the following statement:

If R is total and surjective, then R $$ R$^$T is reflexive.