Explain the flaw in the following “argument.”
All trucks are the same color.
Proof: Let P(n): Any set of n trucks consists of trucks of the same color.
Basis Step: Certainly P(1) is true, since there is only one truck in this case.
Induction Step: We use P(k): Any set of k trucks consists of trucks of the same color to show P(k + 1): Any set of k + 1 trucks consists of trucks of the same color. Choose one truck from the set of k + 1 trucks and consider the remaining set of k trucks. By P(k) these are all the same color. Now return the chosen truck and set aside another truck. The remaining trucks are all the same color by P(k). But trucks do not change color in this procedure, so all k + 1 trucks must be the same color.
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