For any n ≥ 1 let P(n) be the predicate that AnU₁₂₁²_₁ B₂ = U₂₁ (An B₂). i=1 Suppose we're in the middle of a proof by induction that Vn ≥ 1 : P(n). Suppose our first steps of the inductive step for k ≥ 1 are: k+1 i=1 Anu B₁ = An (B₁₁ k+1 U-₁B₂) =1 True False = (AN Bk+1) U (Aѵ¼_₁ B₂) i=1 True or False: Given the information above, we need both P(1) and P(2) (and no more) as base cases in order for this induction proof to work.

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