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No, ($A \times B$) ∪ ($C \times D$) generally does not equal (A ∪ C) × (B ∪ D). While the intersection of two Cartesian products is a Cartesian product, their union is typically an irregular shape (like an L-shape) that cannot be expressed as a single Cartesian product of two sets.

Conditions: A, B, C, and D are arbitrary sets.

No, ($A \times B$) ∪ ($C \times D$) generally does not equal (A ∪ C) × (B ∪ D). While the intersection of two Cartesian products is a Cartesian product, their union is typically an irregular shape (like an L-shape) that cannot be expressed as a single Cartesian product of two sets.

Conditions: A, B, C, and D are arbitrary sets.