  In this paper, we study the dynamics induced by finite commutative relation.
We prove that the dynamics generated by such a non-trivial collection cannot be
transitive/super-transitive and hence cannot exhibit higher degrees of mixing.
As a consequence we establish that the dynamics induced by such a collection on
the hyperspace endowed with any admissible hit and miss topology cannot be
transitive and hence cannot exhibit any form of mixing. We also prove that if
the system is generated by such a commutative collection, under suitable
conditions the induced system cannot have dense set of periodic points. In the
end we give example to show that the induced dynamics in this case may or may
not be sensitive.
