Concept:
In electrolysis, oxidation occurs at the anode and reduction occurs at the cathode. In aqueous \(Na_2SO_4\), water is mainly electrolysed because \(Na^+\) and \(SO_4^{2-}\) ions are difficult to discharge under these conditions.
Step 1: Identify the ions present in aqueous sodium sulphate solution.
\[
Na_2SO_4 \rightarrow 2Na^+ + SO_4^{2-}
\]
Water is also present:
\[
H_2O
\]
Step 2: At the cathode, reduction takes place.
At cathode, water gets reduced more easily than \(Na^+\). Therefore:
\[
2H_2O+2e^- \rightarrow H_2+2OH^-
\]
So gas liberated at cathode is:
\[
Y=H_2
\]
Step 3: At the anode, oxidation takes place.
At anode, water is oxidised to oxygen:
\[
2H_2O \rightarrow O_2+4H^+ +4e^-
\]
So gas liberated at anode is:
\[
X=O_2
\]
Step 4: Therefore:
\[
X=O_2,\qquad Y=H_2
\]
Hence,
\[
\boxed{O_2,\ H_2}
\]