Answer: Induction cannot establish the statement starting from that base case.
- A P(n) remains true for any value of n regardless of the base case outcome
- B Induction cannot establish the statement starting from that base case
- C P(n) is false for this particular natural number, though that alone proves little
- D The inductive step becomes unnecessary here and can safely be skipped over
Correct answer: B. Induction cannot establish the statement starting from that base case
Explanation: If the base case fails, the entire induction argument breaks down since there is no starting domino to knock over.
Mathematical induction works like a row of dominoes: proving the base case P(1) tips the first domino, and proving the inductive step (P(k) ⟹ P(k+1)) guarantees each domino knocks over the next - together these two facts guarantee ALL dominoes fall, without checking each one individually.
Concept context
A proof technique used to establish that a statement is true for every natural number, using a base case and an inductive step.