[Falkner Section 11 Exercise 15(b) – modified] Let S and T be sets. Prove that S and T are disjoint (i.e., SnT = Ø) if and only if the following condition holds: (*) For all subsets A₁, A₂ C S and B₁, B₂ C T, if A₁ U B₁ = A₂ U B2, then A₁ = A2 and B₁ B2₂. =

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