Suppose A = {1, 2, 3} and B = {1, 2}. Which subsets of A × B are of the form X × Y , where
X ⊆ A and Y ⊆ B?

To find subsets of \( A \times B \) that are of the form \( X \times Y \), where \( X \subseteq A \) and \( Y \subseteq B \), we will first compute the Cartesian product \( A \times B \), then identify the subsets of this form.

### Step 1: Compute \( A \times B \)
The Cartesian product \( A \times B \) is the set of all ordered pairs where the first element is from \( A \) and the second element is from \( B \). 

\[
A \times B = \{(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2)\}
\]

### Step 2: Analyze subsets of the form \( X \times Y \)
For \(

Suppose A = {1, 2, 3} and B = {1, 2}. Which subsets of A × B are of the form X × Y, where X ⊆ A and Y ⊆ B?

Explore how to determine which subsets of A × B are of the form X × Y, where A = {1, 2, 3}, B = {1, 2}, and X ⊆ A, Y ⊆ B. This solution involves key concepts in set theory, Cartesian products, and subset analysis, ideal for students in Grades 9-12.

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