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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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
Transcribed Image Text: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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