In the following sets of reactants which two sets best exhibit the amphoteric characters of `Al_(2)O_(3). xH_(2)O` ?
Set `1: Al_(2)O_(3). xH_(2)O (s) and OH^(-) (aq)`
Set `2: Al_(2)O_(3).xH_(2)O(s) and H_(2)O(I)`
Set `3: Al_(2)O_(3). xH_(2)O(s) and H^(+) (aq)`
Set `4: Al_(2)O_(3).xH_(2)O(s) and NH_(3) (aq)`

Options

A. 1 and 2
B. 1 and 3
C. 2 and 4
D. 3 and 4

Explanation

To determine which sets of reactants best exhibit the amphoteric character of `Al_(2)O_(3). xH_(2)O`, we need to analyze the properties of aluminum oxide and how it interacts with acids and bases.

### Step-by-Step Solution:

1. **Understanding Amphoteric Nature**:
- Aluminum oxide (`Al_(2)O_(3)`) is classified as an amphoteric oxide, meaning it can react both as an acid and as a base. It can react with acids to form salts and water, and it can also react with bases to form complex ions.

2. **Analyzing the Sets**:
- **Set 1**: `Al_(2)O_(3). xH_(2)O (s)` and `OH^(-) (aq)`
- Here, `Al_(2)O_(3)` reacts with hydroxide ions (`OH^(-)`), which is a basic reaction. This confirms the amphoteric nature as it can react with a base.
- **Set 2**: `Al_(2)O_(3). xH_(2)O (s)` and `H_(2)O (l)`
- This set does not show a clear reaction that demonstrates amphoteric behavior. Water does not interact significantly with aluminum oxide to exhibit its amphoteric character.
- **Set 3**: `Al_(2)O_(3). xH_(2)O (s)` and `H^(+) (aq)`
- In this case, `Al_(2)O_(3)` reacts with hydrogen ions (`H^(+)`), which is an acidic reaction. This also confirms the amphoteric nature as it can react with an acid.
- **Set 4**: `Al_(2)O_(3). xH_(2)O (s)` and `NH_(3) (aq)`
- Ammonia (`NH_(3)`) is a weak base, but it does not exhibit a strong acid-base reaction with aluminum oxide to demonstrate its amphoteric character.

3. **Conclusion**:
- The sets that best exhibit the amphoteric character of `Al_(2)O_(3). xH_(2)O` are Set 1 (`Al_(2)O_(3). xH_(2)O (s)` and `OH^(-) (aq)`) and Set 3 (`Al_(2)O_(3). xH_(2)O (s)` and `H^(+) (aq)`).
- Therefore, the correct answer is **Set 1 and Set 3**.

### Final Answer:
The two sets that best exhibit the amphoteric character of `Al_(2)O_(3). xH_(2)O` are **Set 1 and Set 3**.