To determine the set difference $(A \times A) \setminus (B \times B)$, we need to follow these steps:

1. Define the Cartesian products $A \times A$ and $B \times B$:

   • $A \times A = \{ (x, y) \mid x \in A \text{ and } y \in A \}$
   • $B \times B = \{ (x, y) \mid x \in B \text{ and } y \in B \}$

   With $A = \{ 0, 3 \}$ and $B = \{ 1, 2 \}$, we can list out each product:

   • $A \times A = \{ (0, 0), (0, 3), (3, 0), (3, 3) \}$
   • $B \times B = \{ (1, 1), (1, 2), (2, 1), (2, 2) \}$

2. Calculate the Set Difference $(A \times A) \setminus (B \times B)$:

   The set difference $(A \times A) \setminus (B \times B)$ consists of all elements in $A \times A$ that are not in $B \times B$.

   Since $A \times A$ and $B \times B$ have no overlapping elements (because $A$ and $B$ have no common values), the entire set $A \times A$ is distinct from $B \times B$. Thus:

   $(A \times A) \setminus (B \times B) = A \times A = \{ (0, 0), (0, 3), (3, 0), (3, 3) \}$

Final Answer

$(A \times A) \setminus (B \times B) = \{ (0, 0), (0, 3), (3, 0), (3, 3) \}$

Would you like further details or have any questions?

---

Here are some related questions for further practice:

1. How would you find $(B \times B) \setminus (A \times A)$?
2. What is $(A \cup B) \times (A \cup B)$?
3. How can you find the intersection $(A \times A) \cap (B \times B)$ if $A$ and $B$ have common elements?
4. What would be the result of $(A \times B) \cup (B \times A)$?
5. How does the Cartesian product behave when $A$ or $B$ is empty?

Tip: In set difference operations, always verify if the sets have any elements in common, as it can simplify calculations!