Concept explainers
rcises 49-51 present incorrect proofs using mathematical induction. You rill need to identify" an error in reasoningin each exercise.
49.What is wrong with this "proof" that all horses are the same color?
LetP(n) be the proposition that all thehorses in a set ofnhorses are the same color.
Basis Step: Clearly,P(1) is true.
Inductive Step: Assume thatP(k) is true, so that all the horses in any set of Morses are the same color. Consider anyk +1 horses; number these as horses 1,,2,3,...,k,k+1. Now the firstk ofthese horses all must have the same color, and the last taf these must also have the same color. Because the set of the first horses and the set of thelast horses overlap, allk+1 must be the same color. This shows thatP(k+1\)is true and finishes the proof by induction.
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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
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