Let $U$ be a non-empty set. We define a mathematical structure on the power set $P(U)$ with two operations:

• Addition: $A \oplus B = A \Delta B$ (symmetric difference)
• Multiplication: $A \odot B = A \cap B$ (intersection)

Which of the following properties does NOT hold for the algebraic ring $(P(U), \oplus, \odot)$?