Statement 1 : The ${\mathrm{H}}_3{\mathrm{O}}^{+}$ has additional water molecules closely associated with it.

Statement 2 : In solid state the species ${\mathrm{H}}_5{\mathrm{O}}_2^{+} \mathrm{and} {\mathrm{H}}_9{\mathrm{O}}_4^{+}$ have been found to exist.

Hydrogen ion is a proton (H⁺), binds it self with the water molecules to form H₃O⁺. Which has been detected in many compounds in the solid state. In aqueous solution the hydronium ion is further hydrated to give species like ${\mathrm{H}}_5{\mathrm{O}}_2^{+} , {\mathrm{H}}_7{\mathrm{O}}_3^{+} , {\mathrm{H}}_9{\mathrm{O}}_4^{+}.$