I and II are present in all options so need to check.
For III and IV
$(P∧Q)∨(P∧\neg Q) \equiv P∧(Q \vee\neg Q)$ (By distributive law)
$\quad \quad \equiv P∧T$
$\quad \quad \equiv P$
For III.
$P∨( \neg P∧\neg Q) \equiv P\vee \neg Q$ (By Absorption Law)
For IV.
$P∨(¬P∧Q) \equiv P∨Q$ (By Absorption Law)
So Option B is correct.
I, II, III are logically equivalent.