   Chapter 11.2, Problem 1ES ### 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 Ω − notation, written using quantifiers and variables: f ( n ) if, and only if, ∃ positive real numbers a and A such that ∀ n ≥ a ,   A g ( n ) ≤ f ( n ) .a. Write the formal negation for the definition using the symbols ∀ and ∃ .b. Restate the negation less formally without using the symbols ∀ and ∃ or the words “for any,” “for every,” or “there exists.”

To determine

(a)

To show:

Write the formal negation for the defintion using the symbols and .

Explanation

Given information:

The following is a formula definition for Ω(g(x)) if, and only if, positive real numbers a and A such that x>a,A|g(x)|f(x)|.

Concept used:

Positive real numbers a and A.

Calculation:

Positive real numbers a and A

To determine

(b)

Restate the negation less formally without using the symbols  and .

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