If n(A)=x and n(B)=y and `AcapB=phi` then `n(AxxB)=xy`.

Answer

To solve the problem, we need to prove that if \( n(A) = x \) and \( n(B) = y \) with \( A \cap B = \phi \) (meaning sets A and B are disjoint), then \( n(A \times B) = xy \).

### Step-by-Step Solution:

1. **Understanding the Sets**:
- We have two sets, \( A \) and \( B \).
- The number of elements in set \( A \) is given as \( n(A) = x \).
- The number of elements in set \( B \) is given as \( n(B) = y \).
- The intersection of sets \( A \) and \( B \) is empty, which means \( A \) and \( B \) have no elements in common: \( A \cap B = \phi \).

2. **Definition of Cartesian Product**:
- The Cartesian product \( A \times B \) is defined as the set of all ordered pairs \( (a, b) \) where \( a \) is an element of \( A \) and \( b \) is an element of \( B \).
- Mathematically, \( A \times B = \{ (a, b) | a \in A, b \in B \} \).

3. **Calculating the Number of Elements in the Cartesian Product**:
- To find the number of elements in the Cartesian product \( A \times B \), we use the formula:
\[ n(A \times B) = n(A) \cdot n(B) \]
- Since we know \( n(A) = x \) and \( n(B) = y \), we can substitute these values into the formula:
\[ n(A \times B) = x \cdot y \]

4. **Conclusion**:
- Therefore, we have shown that \( n(A \times B) = xy \).
- Since the condition \( A \cap B = \phi \) does not affect the calculation of the Cartesian product, the statement is true.

### Final Answer:
The statement is true: \( n(A \times B) = xy \).

---