Consider the following recurrence relation: P(n) = {. p(n-1) + 1 Jo Prove by induction that P(n) = 5n -¹ for all n ≥ 0. (Induction on n.) Let f(n) = 5n -1₁ 0 Base Case: If n = 0, the recurrence relation says that P(0) = 0, and the formula says that f(0) = Inductive Hypothesis: Suppose as inductive hypothesis that P(k-1) = 5(p(k)+1) Inductive Step: Using the recurrence relation, P(K) 5. P(k-1) + 1, by the second part of the recurrence relation = 5 5*-1-1 4 if n = 0 if n > 0. - 5k-5 +4 1 4 + 1, by inductive hypothesis X 4 for some k > 0. ✓ , so they match.

Consider the following recurrence relation: P(n) = {. p(n-1) + 1 Jo Prove by induction that P(n) = 5n -¹ for all n ≥ 0. (Induction on n.) Let f(n) = 5n -1₁ 0 Base Case: If n = 0, the recurrence relation says that P(0) = 0, and the formula says that f(0) = Inductive Hypothesis: Suppose as inductive hypothesis that P(k-1) = 5(p(k)+1) Inductive Step: Using the recurrence relation, P(K) 5. P(k-1) + 1, by the second part of the recurrence relation = 5 5*-1-1 4 if n = 0 if n > 0. - 5k-5 +4 1 4 + 1, by inductive hypothesis X 4 for some k > 0. ✓ , so they match.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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