In the following sets of reactants which two sets best exhibit the amphoteric character of ${\mathrm{Al}}_2{\mathrm{O}}_3.{\mathrm{xH}}_2\mathrm{O}$ ? 

Set1:${\mathrm{Al}}_2{\mathrm{O}}_3.{\mathrm{xH}}_2\mathrm{O}$ and ${\mathrm{OH}}^{-}$

Set2: ${\mathrm{Al}}_2{\mathrm{O}}_3.{\mathrm{xH}}_2\mathrm{O}$ and ${\mathrm{H}}_2\mathrm{O}$

Set3: ${\mathrm{Al}}_2{\mathrm{O}}_3.{\mathrm{xH}}_2\mathrm{O}$ and ${\mathrm{H}}^{+}$

Set4: ${\mathrm{Al}}_2{\mathrm{O}}_3.{\mathrm{xH}}_2\mathrm{O}$ and ${\mathrm{NH}}_3$

Compounds with amphoteric properties are those that react with both acids and salt. Aluminum oxide is essentially an inorganic salt that is used as an antacid.
Aluminum oxide, as we are all aware, exhibits the characteristics of both basic and acidic oxides, making it an amphoteric oxide.
It is discovered that it reacts to produce the equivalent salt and water when combined with both acids and bases.

Aluminum oxide is an amphoteric oxide. It can react with both acid and base. In the given sets amphoteric nature can be explained by taking an acidic reaction and basic reaction. So, aluminum oxide reacts with a proton in set 3 as a base. Similarly, aluminum oxide reacts with hydroxyl ions in set 1 as acid. Thus set 1 and 3 are chosen.

Hence, option A is correct.