Step 1: Concept In the electrolysis of aqueous $Na_{2}SO_{4}$, water is oxidized at the anode and reduced at the cathode because $Na^{+}$ and $SO_{4}^{2-}$ have higher discharge potentials than water.
Step 2: Meaning Anode (Oxidation): $2H_{2}O \to O_{2} + 4H^{+} + 4e^{-}$.
Cathode (Reduction): $2H_{2}O + 2e^{-} \to H_{2} + 2OH^{-}$.
Step 3: Analysis Gas X (Anode) is Oxygen ($O_{2}$). Gas Y (Cathode) is Hydrogen ($H_{2}$).
Step 4: Conclusion The gases are $O_{2}$ and $H_{2}$ respectively.
Final Answer: (B)