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Set Theoryhard
0:00.0

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

  • Addition: A⊕B=AΔBA \oplus B = A \Delta BA⊕B=AΔB (symmetric difference)
  • Multiplication: A⊙B=A∩BA \odot B = A \cap BA⊙B=A∩B (intersection)

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