Write the reactions for the following electrolytic processes:
$A$. Electrolytic reaction of concentrated aqueous solution of $NaCl$ (Brine).
$B$. Electrolytic reaction of dilute aqueous solution of $NaCl$.

(N/A) For $A$ (Concentrated $NaCl$ solution):
At cathode: $2H_2O(l) + 2e^- \rightarrow H_2(g) + 2OH^-(aq)$
At anode: $2Cl^-(aq) \rightarrow Cl_2(g) + 2e^-$
Overall reaction: $2NaCl(aq) + 2H_2O(l) \rightarrow 2Na^+(aq) + 2OH^-(aq) + H_2(g) + Cl_2(g)$
For $B$ (Dilute $NaCl$ solution):
At cathode: $2H_2O(l) + 2e^- \rightarrow H_2(g) + 2OH^-(aq)$
At anode: $2H_2O(l) \rightarrow O_2(g) + 4H^+(aq) + 4e^-$
Overall reaction: $2H_2O(l) \rightarrow 2H_2(g) + O_2(g)$