Suppose that in a proof by strong induction, the following statement is the inductivehypothesis: For k ≥ 6, P(j) is true for any j in the range {4,5,..., k}.If k is an integer, and k ≥ 6, then which of the following statements can you assume to be true? Clearlyjustify your choice.(a) P(k − 1) but not P(k − 2) or P(k − 3)(b) P(k − 3), P(k − 2), and P(k − 1)(c) None of P(k − 3), P(k − 2), or P(k − 1)(d) P(k − 2) and P(k − 1) but not P(k − 3)

Answered: For k ≥ 6, P(j) is true for any j in…

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 that in a proof by strong induction, the following statement is the inductive

hypothesis:

For k ≥ 6, P(j) is true for any j in the range {4,5,..., k}.
If k is an integer, and k ≥ 6, then which of the following statements can you assume to be true? Clearly
justify your choice.
(a) P(k − 1) but not P(k − 2) or P(k − 3)
(b) P(k − 3), P(k − 2), and P(k − 1)
(c) None of P(k − 3), P(k − 2), or P(k − 1)
(d) P(k − 2) and P(k − 1) but not P(k − 3)

Expert Solution

Step 1

Here the question is from the concept of mathematical induction.

Here let's assume k as its least possible value, that is 6 (It is given that $k \geq 6$ )

The inductive statement given in the question is:

$F o r k \geq 6, P (j) i s t r u e f o r a n y j i n r a n g e {4, 5, . . . ., k}$

from this statement, it is understandable that in order to maintain(ensure more correctly) the truth value of P, j should be in the range { 4, 5, ...., k}

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