Statement-1 If `AuuB=AuuC` and `AnnB=AnnC`, then B = C.
Statement-2 `Auu(BnnC)=(AuuB)nn(AuuC)`

Explanation

To solve the given problem, we need to analyze both statements and determine their validity step by step.

### Step 1: Analyze Statement 1
**Statement 1:** If \( A \cup B = A \cup C \) and \( A \cap B = A \cap C \), then \( B = C \).

1. **Given Sets:**
- Let \( A = \{1, 2, 3, 4\} \)
- Let \( B = \{4, 5, 6\} \)
- Let \( C = \{4, 5, 6\} \)

2. **Calculate \( A \cup B \) and \( A \cup C \):**
- \( A \cup B = \{1, 2, 3, 4\} \cup \{4, 5, 6\} = \{1, 2, 3, 4, 5, 6\} \)
- \( A \cup C = \{1, 2, 3, 4\} \cup \{4, 5, 6\} = \{1, 2, 3, 4, 5, 6\} \)

3. **Check \( A \cap B \) and \( A \cap C \):**
- \( A \cap B = \{1, 2, 3, 4\} \cap \{4, 5, 6\} = \{4\} \)
- \( A \cap C = \{1, 2, 3, 4\} \cap \{4, 5, 6\} = \{4\} \)

4. **Conclusion for Statement 1:**
- Since \( A \cup B = A \cup C \) and \( A \cap B = A \cap C \), we can conclude that \( B = C \).

### Step 2: Analyze Statement 2
**Statement 2:** \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C) \)

1. **Given Sets:**
- Let \( A = \{1, 2, 3, 4\} \)
- Let \( B = \{4, 5, 6\} \)
- Let \( C = \{5, 6, 7\} \)

2. **Calculate \( B \cap C \):**
- \( B \cap C = \{4, 5, 6\} \cap \{5, 6, 7\} = \{5, 6\} \)

3. **Calculate \( A \cup (B \cap C) \):**
- \( A \cup (B \cap C) = \{1, 2, 3, 4\} \cup \{5, 6\} = \{1, 2, 3, 4, 5, 6\} \)

4. **Calculate \( A \cup B \) and \( A \cup C \):**
- \( A \cup B = \{1, 2, 3, 4\} \cup \{4, 5, 6\} = \{1, 2, 3, 4, 5, 6\} \)
- \( A \cup C = \{1, 2, 3, 4\} \cup \{5, 6, 7\} = \{1, 2, 3, 4, 5, 6, 7\} \)

5. **Calculate \( (A \cup B) \cap (A \cup C) \):**
- \( (A \cup B) \cap (A \cup C) = \{1, 2, 3, 4, 5, 6\} \cap \{1, 2, 3, 4, 5, 6, 7\} = \{1, 2, 3, 4, 5, 6\} \)

6. **Conclusion for Statement 2:**
- Since both sides are equal, \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C) \) is true.

### Final Conclusion
- **Statement 1 is true:** If \( A \cup B = A \cup C \) and \( A \cap B = A \cap C \), then \( B = C \).
- **Statement 2 is true:** \( A \cup (B \cap C) = (A \cup B) \cap (A \cup C) \).