To solve the problem and visualize it, let's break down each part:

1. Define $A$ and $B$:

   • Set $A = \{0, 3\}$ and $B = \{1, 2\}$.

2. Construct the Cartesian Products $A \times A$ and $B \times B$:

   • $A \times A$ is the set of all ordered pairs where each element comes from $A$. $A \times A = \{(0, 0), (0, 3), (3, 0), (3, 3)\}$
   • $B \times B$ is the set of all ordered pairs where each element comes from $B$. $B \times B = \{(1, 1), (1, 2), (2, 1), (2, 2)\}$

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

   • This difference means we take all elements in $A \times A$ that are not in $B \times B$.
   • Since there are no common pairs between $A \times A$ and $B \times B$, we find that: $(A \times A) \setminus (B \times B) = A \times A = \{(0, 0), (0, 3), (3, 0), (3, 3)\}$

4. Draw Pictures:

   • For visualization, we can plot the pairs in $A \times A$ and $B \times B$ on a grid to represent each point.
   • The pairs in $A \times A$ will be plotted separately from those in $B \times B$ to show the distinction between the sets.

Let's create the visualization. I'll generate the plot for these points.Here is the visualization:

• Blue points represent the pairs in $A \times A = \{(0, 0), (0, 3), (3, 0), (3, 3)\}$.
• Red points represent the pairs in $B \times B = \{(1, 1), (1, 2), (2, 1), (2, 2)\}$.

Since there are no common points between $A \times A$ and $B \times B$, the set difference $(A \times A) \setminus (B \times B)$ is simply all the blue points in $A \times A$.

Would you like further details on any part of this solution?

Here are some follow-up questions to consider:

1. What is the significance of Cartesian products in set theory?
2. How would the solution change if $A$ and $B$ had overlapping elements?
3. What does the operation $\setminus$ mean for sets in general?
4. How would you calculate $(A \times B) \setminus (B \times A)$?
5. Could we represent these Cartesian products in other dimensions?

Tip: When visualizing Cartesian products, try to distinguish sets with different colors for clarity.