Which among the following is correct for electrolysis of brine solution?

In electrolysis of brine solution, $H_2$ gas is liberated at cathode. The solution contains four ions $N{a}^{+},C{l}^{\theta },H^{+}$ and $\stackrel{\theta }{O}H$ ions. There occurs a race amongst them for their discharge at their respective electrodes.
Following electrode reactions are possible:
$\mathbf{C}\mathbf{a}\mathbf{t}\mathbf{h}\mathbf{o}\mathbf{d}\mathbf{e}2H_{2}O\left(l\right)+2e^{-}\to H_2\left(g\right)+2\stackrel{-}{O}H\left(aq\right)$
$\mathbf{A}\mathbf{n}\mathbf{o}\mathbf{d}\mathbf{e}2C{l}^{-}\left(aq\right)\to C{l}_2\left(g\right)+2e^{-}$
In this electrolysis, $H_2$ at cathode and $C{l}_2$ at anode are given off.