Step 1: Recall the product of Solvay's process.
Solvay's process is the industrial method for manufacturing
\[
\boxed{\mathrm{Na_2CO_3}}
\]
(sodium carbonate).
Hence,
\[
X=\mathrm{Na_2CO_3}.
\]
Step 2: Recall the product of Castner-Kellner process.
Castner-Kellner process is used for the manufacture of
\[
\boxed{\mathrm{NaOH}}
\]
(sodium hydroxide) by electrolysis of brine.
Hence,
\[
Y=\mathrm{NaOH}.
\]
Step 3: Write the answer.
Therefore,
\[
X=\mathrm{Na_2CO_3},
\qquad
Y=\mathrm{NaOH}.
\]
Hence,
\[
\boxed{\mathrm{Na_2CO_3,\ NaOH}}.
\]
Thus,
\[
\boxed{(D)}
\]
is the correct answer.