Statement I : Boric acid is a Protonic acid

Statement II : Aqueous solution of boric acid contains a proton

Statement I) Boric acid has no replacable H–atoms. It is not a Protonic acid

Statement –II) $\mathrm{B}{\left(\mathrm{OH}\right)}_3+{\mathrm{H}}_2\mathrm{O} \rightleftharpoons {\left[\mathrm{B}{\left(\mathrm{OH}\right)}_4\right]}^{-}+{\mathrm{H}}^{+}$

It accepts ${\mathrm{OH}}^{-}$ ions from water and thus the ${\mathrm{H}}^{+}$ ion of water will be present in aqueous solution.