Step 1: Identify intermediate \(X\).
Tert-butyl alcohol on dehydration gives
\[
\boxed{\mathrm{2\mbox{-}methylpropene}.}
\]
Both
\[
\mathrm{Cu/573\,K}
\]
and
\[
20\%\mathrm{H_3PO_4}/358\,K
\]
produce this alkene.
Step 2: Check the conversion to the final product.
Set II:
\[
\mathrm{HBr/(C_6H_5CO)_2O_2}
\]
adds HBr by the peroxide effect to form the anti-Markovnikov product, which on hydrolysis gives
\[
\mathrm{(CH_3)_2CHCH_2OH}.
\]
Hence, Set II is correct.
Step 3: Check Set III.
Hydroboration-oxidation,
\[
(\mathrm{BH_3})_2,\ \mathrm{H_2O_2/OH^-},
\]
directly gives the anti-Markovnikov alcohol
\[
\mathrm{(CH_3)_2CHCH_2OH}.
\]
Hence, Set III is correct.
Step 4: Reject the remaining sets.
Sets I and IV involve Markovnikov addition of HBr followed by hydrolysis, leading to tert-butyl alcohol rather than the required major product.
Hence, they are incorrect.
Therefore,
\[
\boxed{\text{II and III only}}
\]
are correct.
Thus,
\[
\boxed{(D)}
\]
is the correct answer.