  In this paper we have mainly focused on the uniqueness of two meromorphic
functions under the realm of two shared sets problem with certain restrictions
which in turn improve the results of { P. Sahoo and H. Karmakar, Uniqueness
theorems related to weighted sharing of two sets, Acta Univ. Sapientiae,
Mathematica, 10(2) (2018), 329-339} and {P. Sahoo and A. Sarkar, On the
uniqueness of meromorphic functions sharing two sets, Bol. Soc. Mat. Mex.,
(2019), 1-7}. In particular, pointing out some gaps in the statements of the
results in { P. Sahoo and H. Karmakar, Uniqueness theorems related to weighted
sharing of two sets, Acta Univ. Sapientiae, Mathematica, 10(2) (2018), 329-339}
and {P. Sahoo and A. Sarkar, On the uniqueness of meromorphic functions sharing
two sets, Bol. Soc. Mat. Mex., (2019), 1-7}. we have removed the order
restrictions on the main results in { P. Sahoo and H. Karmakar, Uniqueness
theorems related to weighted sharing of two sets, Acta Univ. Sapientiae,
Mathematica, 10(2) (2018), 329-339} and {P. Sahoo and A. Sarkar, On the
uniqueness of meromorphic functions sharing two sets, Bol. Soc. Mat. Mex.,
(2019), 1-7} at the cost of sharing of an additional singleton. A number of
examples have been provided by us to show some conditions in our results are
essential.
