Answer: Showing that if P(k) is true, then P(k+1) is also true.
- A Proving P(1) only, without considering any later case
- B Showing that if P(k) is true, then P(k+1) is also true
- C Proving P(n) directly for one specific, large chosen n
- D Disproving P(k) to show the statement fails in general
Correct answer: B. Showing that if P(k) is true, then P(k+1) is also true
Explanation: The inductive step is a conditional proof: assuming P(k), it shows P(k+1) must follow.
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.