Write the reactions for the following processes:
$A$. Electrolysis of water at the anode and cathode.
$B$. Electrolytic reaction of molten $NaCl$.

For $A$. Electrolysis of water:
At the anode (oxidation): $2H_2O(l) \rightarrow O_2(g) + 4H^+(aq) + 4e^-$
At the cathode (reduction): $4H_2O(l) + 4e^- \rightarrow 2H_2(g) + 4OH^-(aq)$
Overall reaction: $2H_2O(l) \rightarrow 2H_2(g) + O_2(g)$
For $B$. Electrolysis of molten $NaCl$:
At the anode (oxidation): $2Cl^-(l) \rightarrow Cl_2(g) + 2e^-$
At the cathode (reduction): $2Na^+(l) + 2e^- \rightarrow 2Na(l)$
Overall reaction: $2NaCl(l) \rightarrow 2Na(l) + Cl_2(g)$