I and II are present in each option so need to check.
For III and IV
(P∧Q)∨(P∧~ Q) = P∧(QV~Q) (By distributive law)
= P∧T
=P
For III.
P∨( ~P∧~Q) = P∨~Q (By Absorption Law)
For IV.
P∨(¬P∧Q) = P∨Q (By Absorption Law)
So Option B is correct.
I, II, III are logically equivalent.