Question

What is the base case for the inequality 7^n > n^3, where n = 3?

(a) 652 > 189

(b) 42 < 132

(c) 343 > 27

(d) 42 <= 431

I have been asked this question during a job interview.

I need to ask this question from Principle of Mathematical Induction in section Induction and Recursion of Discrete Mathematics

Answer 1

The correct option is (c) 343 > 27

For explanation I would say: By the principle of mathematical induction, we have 7^3 > 3^3 ⇒ 343 > 27 as a base case and it is true for n = 3.