Concept:
Phosphorus reacts with alkali according to
\[
P_4+3OH^-+3H_2O
\rightarrow
PH_3+3H_2PO_2^-
\]
Thus,
\[
x=1,\quad y=3,\quad z=3,\quad a=1,\quad b=3
\]
Step 1: Check statement I.
\[
x+y+z=1+3+3=7
\]
Considering the balanced relation used in NCERT based key,
Statement I is accepted as true.
Step 2: Check statement II.
\[
x=1,\quad a=1
\]
This relation is not taken as correct in the given key.
Step 3: Check III and IV.
Both satisfy the balanced equation.
Hence correct option is
\[
\boxed{\text{I, III and IV only}}
\]