Suppose we have a recursive sequence f1, f2, f3,....For the purposes of this problem, it does not matter exactly how the f; are defined,only that they are recursively defined.For integer n ≥ 1, let P(n) be the predicate that fn = 2n². Don't worryabout whether this predicate "makes sense"; we haven't defined the f; so you won'tbe able to "make sense" of the P(n). It's not important for this problem.Consider a proof by induction that Vn 1: P(n).Suppose that the first step of the inductive step isfk+1 = (k − 1) · fkTrue or false: Based on the information given, we will need at least P(1), P(2) as basecases for this proof.TrueFalse

Answered: at least P(1), P(2) as base

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at least P(1), P(2) as base

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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Question

Suppose we have a recursive sequence f1, f2, f3,....
For the purposes of this problem, it does not matter exactly how the f; are defined,
only that they are recursively defined.
For integer n ≥ 1, let P(n) be the predicate that fn = 2n². Don't worry
about whether this predicate "makes sense"; we haven't defined the f; so you won't
be able to "make sense" of the P(n). It's not important for this problem.
Consider a proof by induction that Vn 1: P(n).
Suppose that the first step of the inductive step is
fk+1 = (k − 1) · fk
True or false: Based on the information given, we will need at least P(1), P(2) as base
cases for this proof.
True
False

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