need help with the 2 boxes with x mark Consider the following recurrence relation:=C(n) =) = {0+3. C(n-1) ifn>0.Prove by induction that C(n) = 3+1 -2n-3 for all n ≥ 0.4(Induction on n.) Let f(n) = 3n+1 - 2n-Base Case: If n = 0, the recurrence relation says that C(0) = 0, and the formula says that f(0) ==k+ 3.1Inductive Hypothesis: Suppose as inductive hypothesis that C(k-1)=f(k-1)AKInductive Step: Using the recurrence relation,C(k)=k+ 3 C(k-1), by the second part of the recurrence relation-33+1-6k-343−1+1 -2(k-1) – 3443k+1-2k-34Xby inductive hypothesisX0+1for some k > 0.4-2.0-30✓, so they match.

Recurrence Relation: A recurrence relation is an equation with rules that represents a…

Consider the following recurrence relation: if n = 0 if n > 0. C(n) = - {1+3.0 (n+3·C(n-1) Prove by induction that C(n) = 3n+1-2n - 3 for all n ≥ 0. 4 3n+1 - 2n (Induction on n.) Let f(n) = Base Case: If n = 0, the recurrence relation says that C(0) = 0, and the formula says that f(0) = Inductive Hypothesis: Suppose as inductive hypothesis that C(k-1) = f(k-1) =k+ 3. Inductive Step: Using the recurrence relation, C(K) = k + 3. C(k-1), by the second part of the recurrence relation 3-1+1-2(k-1)-3 4 3²+1 -3 4 -6k-3 4 X 4 3+1-2k-3 by inductive hypothesis X 0+1 for some k > 0. - 2.0 0 ✓ , so they match.

Consider the following recurrence relation: if n = 0 if n > 0. C(n) = - {1+3.0 (n+3·C(n-1) Prove by induction that C(n) = 3n+1-2n - 3 for all n ≥ 0. 4 3n+1 - 2n (Induction on n.) Let f(n) = Base Case: If n = 0, the recurrence relation says that C(0) = 0, and the formula says that f(0) = Inductive Hypothesis: Suppose as inductive hypothesis that C(k-1) = f(k-1) =k+ 3. Inductive Step: Using the recurrence relation, C(K) = k + 3. C(k-1), by the second part of the recurrence relation 3-1+1-2(k-1)-3 4 3²+1 -3 4 -6k-3 4 X 4 3+1-2k-3 by inductive hypothesis X 0+1 for some k > 0. - 2.0 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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Concept explainers

Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.

Question

need help with the 2 boxes with x mark

Consider the following recurrence relation:
=
C(n) =
) = {0+3. C(n-1) ifn>0.
Prove by induction that C(n) = 3+1 -2n-3 for all n ≥ 0.
4
(Induction on n.) Let f(n) = 3n+1 - 2n-
Base Case: If n = 0, the recurrence relation says that C(0) = 0, and the formula says that f(0) =
=k+ 3.1
Inductive Hypothesis: Suppose as inductive hypothesis that C(k-1)=f(k-1)
AK
Inductive Step: Using the recurrence relation,
C(k)=k+ 3 C(k-1), by the second part of the recurrence relation
-3
3+1-6k-3
4
3−1+1 -2(k-1) – 3
4
4
3k+1-2k-3
4
X
by inductive hypothesis
X
0+1
for some k > 0.
4
-2.0-3
0
✓
, so they match.

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