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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.

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.

To compute the Cartesian product of two finite sets, systematically pair each element of the first set with every element of the second set, and list all resulting ordered pairs in a new set.

Conditions: The sets are finite and explicitly given.

To compute the Cartesian product of two finite sets, systematically pair each element of the first set with every element of the second set, and list all resulting ordered pairs in a new set.

Conditions: The sets are finite and explicitly given.