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CSCE 222 CSCE222 Problem Set 6 – Texas A&M

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CSCE 222 CSCE222 Problem Set 6 – Texas A&M

Problem Set 6

Resources.(All people, books, articles, web pages, etc. that have been con-sulted when producing this homework)

Problem 1.(20 pts) Section 5.3, Exercise 6, page 357

Solution..

(a)

f(0) = 1

f(1) =f(0) =1

f(2) =f(1) = 1

f(3) =f(2) =1

f(n) = (1)n

Basis Step:f(0) = 1 = (1)0

Inductive step:

if f(n)

Description

CSCE 222 CSCE222 Problem Set 6 – Texas A&M

Problem Set 6

Resources.(All people, books, articles, web pages, etc. that have been con-sulted when producing this homework)

Problem 1.(20 pts) Section 5.3, Exercise 6, page 357

Solution..

(a)

f(0) = 1

f(1) =f(0) =1

f(2) =f(1) = 1

f(3) =f(2) =1

f(n) = (1)n

Basis Step:f(0) = 1 = (1)0

Inductive step:

if f(n) = (1)n, then

f(n+ 1) =f(n)

f(n+ 1) =(1)n

f(n+ 1) = (1)n+1

(b) Not a valid recursive definition.

(c) Not a valid recursive definition.

(d)

f(0) = 0

f(1) = 1

f(2) = 2

f(1) = 2

f(3) = 2

f(2) = 4

f(n) = 2n1

(e)

f(0) = 2

f(1) =f(0) = 2

f(2) = 2f(0) = 4

f(3) =f(2) = 4

f(4) = 2f(2) = 8

f(5) =f(4) = 8

f(6) = 2f(4) = 16

f(n) = 21+bn2c

Problem 2.(20 pts) Section 5.3, Exercise 8, page 358

Solution

CSCE 222 CSCE222 Problem Set 6 – Texas A&M

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