Answer: 2 > 1, which is true.
- A 2 > 1, which is true
- B 2 < 1, which is false
- C 1 = 1 exactly
- D 0 > 1 falsely
Correct answer: A. 2 > 1, which is true
Explanation: At n = 1, 2¹ = 2 > 1, so the base case holds.
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.