R is a reflexive reation on set A
If system is transitive following should be true
if aRb and bRc then aRc
and it is given to us that
if aRb and bRc then cRa
hence, if system is transitive then it has to be symmetric.
If system is symmetric then if aRc then cRa has to be true
if aRb and bRc then cRa is given to us,
if system is symmetric then following has to be true
if aRb and bRc then aRc. means system has to be transitive
a & b are not possible!
(c) will be true if at least we know that either system is symmetric or transitive. but there is no such info given to us.
I think (d) will be correct answer, because we don't know if system is symmetric or transitive.