   Chapter 11.2, Problem 3ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# The following is a formal definition for Θ -notation, written using quantifiers and variables: f ( n ) is Θ ( g ( n ) ) if, and only if, ∃ positive real numbers k, A, and B such that ∀ n ≥ k ,   A g ( n ) ≤ f ( n ) ≤ B g ( n ) a. Write the formal negation for the definition using the symbols ∀ and ∃ . b. Restate the negation less formally without usi ng the symbols ∀ and ∃ or the words “for any,” “for every,” or “there exists.”

To determine

(a)

To show:

Write the rormal negation for the definition using the symbols  and .

Explanation

Given information:

The following is a formula definition for Θ if, and only if, positive real numbers k

A and B such that x>k,A|g(x)|f(x)|B|g(x)|.

Concept used:

Positive real numbers a and A

To determine

(b)

Restate the negation less formally wahout using the symbols  and

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