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The Cartesian product distributes over both union and intersection from both the left and the right. Specifically, (A ∪ B) × $C = (A \times C)$ ∪ ($B \times C$), (A ∩ B) × $C = (A \times C)$ ∩ ($B \times C$), A × (B ∪ C) = ($A \times B$) ∪ ($A \times C$), and A × (B ∩ C) = ($A \times B$) ∩ ($A \times C$).

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

The Cartesian product distributes over both union and intersection from both the left and the right. Specifically, (A ∪ B) × $C = (A \times C)$ ∪ ($B \times C$), (A ∩ B) × $C = (A \times C)$ ∩ ($B \times C$), A × (B ∪ C) = ($A \times B$) ∪ ($A \times C$), and A × (B ∩ C) = ($A \times B$) ∩ ($A \times C$).

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

The intersection of two Cartesian products ($A \times B$) and ($C \times D$) is equal to the Cartesian product of the intersections of their respective component sets, i.e., (A ∩ C) × (B ∩ D).

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

The intersection of two Cartesian products ($A \times B$) and ($C \times D$) is equal to the Cartesian product of the intersections of their respective component sets, i.e., (A ∩ C) × (B ∩ D).

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