# Prove Theorem 11.2.8: a. Let f and g be real-valued functions defined on the same set of nonnegative integers, and suppose there is a positive real number r such that f ( n ) ≥ 0 and g ( n ) &gt; 0 for every integer n ≥ r . If f ( n ) is Ω ( g ( n ) ) and c is any positive real number, then c f ( n ) is Ω ( g ( n ) ) . b. Let f and g be real-valued functions defined on the same set of nonnegative integers, and suppose there is a positive real number r such that f ( n ) ≥ 0 and g ( n ) ≥ 0 for every integer n ≥ r . If f ( n ) is O ( g ( n ) ) and c is any positive real number, then c f ( n ) is O ( g ( n ) ) . c. Let f and g be real-valued functions defined on the same set of nonnegative integers, and suppose there is a positive real number r such that f ( n ) ≥ 0 and g ( n ) ≥ 0 for every integer n ≥ r . If f ( n ) is Θ ( g ( n ) ) and c is any positive real number, then c f ( n ) is Θ ( g ( n ) ) .

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section
Chapter 11.2, Problem 50ES
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