If A and B are non-empty sets, then `AxxB` is a non-empty set of ordered pairs (x,y) such that `x inB` and `yinA`.

Answer

To solve the problem, we need to determine if the statement regarding the Cartesian product of two non-empty sets A and B is true or false. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Sets**:
- Let A and B be two non-empty sets.
- Since they are non-empty, we know that both sets contain at least one element.

2. **Definition of Cartesian Product**:
- The Cartesian product of two sets A and B, denoted as \( A \times B \), is defined as the set of all ordered pairs \( (x, y) \) where \( x \in A \) and \( y \in B \).

3. **Counting Elements**:
- If the number of elements in set A is denoted as \( n(A) = x \) and the number of elements in set B is denoted as \( n(B) = y \), then the number of elements in the Cartesian product \( A \times B \) can be calculated using the formula:
\[ n(A \times B) = n(A) \times n(B) = x \times y \]

4. **Conclusion**:
- Since both A and B are non-empty, \( x \) and \( y \) are both greater than 0. Therefore, \( x \times y \) is also greater than 0, which means \( A \times B \) is a non-empty set.
- Thus, the statement that \( A \times B \) is a non-empty set of ordered pairs \( (x, y) \) such that \( x \in A \) and \( y \in B \) is **true**.

### Final Answer:
The statement is **true**.

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