Statement E is the only wrong statement in this list. A is correct because induction proofs typically start by verifying the statement for the first natural number in the domain. B is correct since the induction step assumes P(k) and proves P(k+1). C correctly states that if the base and step are valid, the result holds for all relevant n. D is true because induction is a method for proving infinitely many cases using a finite argument. E is false because without proving the base case, there is no guarantee that the chain of implications starts, so the induction proof is incomplete.
Option A:
Option A is incorrect since it claims A alone is wrong, but A accurately describes the base step of induction. Declaring it wrong contradicts standard textbook presentations.
Option B:
Option B is wrong because it treats both A and E as wrong. While E is indeed incorrect, A is a true description of the base case and so cannot be grouped with E as wrong.
Option C:
Option C is correct because it singles out E, which wrongly dismisses the need for a base case, as the only incorrect statement. The other statements together present a coherent picture of mathematical induction.
Option D:
Option D is incorrect because it adds A and C to E in the set of wrong statements. C is a true summary of the outcome of induction, and A correctly describes the base step, so this option misclassifies several true statements as wrong.
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