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The distributive law (A ∪ B) × $C = (A \times C)$ ∪ ($B \times C$) can be understood by treating sets as lengths of line segments and Cartesian products as areas of rectangles. The area of a large rectangle with width A ∪ B and height C equals the sum of the areas of two smaller rectangles with widths A and B, and height C.

Conditions: A, B, and C are arbitrary sets.; The geometric analogy treats sets as lengths and Cartesian products as rectangular areas.

The distributive law (A ∪ B) × $C = (A \times C)$ ∪ ($B \times C$) can be understood by treating sets as lengths of line segments and Cartesian products as areas of rectangles. The area of a large rectangle with width A ∪ B and height C equals the sum of the areas of two smaller rectangles with widths A and B, and height C.

Conditions: A, B, and C are arbitrary sets.; The geometric analogy treats sets as lengths and Cartesian products as rectangular areas.

The property ($A \times B$) ∩ ($C \times D$) = (A ∩ C) × (B ∩ D) can be understood by representing Cartesian products as rectangles. The intersection of two rectangles is a smaller rectangle whose width is the intersection of the widths of the original rectangles, and whose height is the intersection of their heights.

Conditions: A, B, C, and D are arbitrary sets.; The geometric analogy treats sets as lengths and Cartesian products as rectangular areas.

The property ($A \times B$) ∩ ($C \times D$) = (A ∩ C) × (B ∩ D) can be understood by representing Cartesian products as rectangles. The intersection of two rectangles is a smaller rectangle whose width is the intersection of the widths of the original rectangles, and whose height is the intersection of their heights.

Conditions: A, B, C, and D are arbitrary sets.; The geometric analogy treats sets as lengths and Cartesian products as rectangular areas.