Let A₁, A₂, . . . be an arbitrary infinite sequence of events, and let B₁, B₂, . . . be another infinite sequence of events defined as follows: B₁ = A₁, B₂ = A^c₁ ∩ A₂, B₃ = A^c₁ ∩ A^c₂ ∩ A₃, B₄ = A^c₁ ∩ A^c₂ ∩ A^c₃ ∩ A₄, . . . . Prove that

And that

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Pr(UA)-EMA).