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Let p(x), q(x), and r(x) denote the following open statements. p(x): x^2-8x+15=0; q(x): x is odd; r(x): x>0; Universe: Integers Determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample. 8a. For all x [p(x)->g(x)]:

Let p(x), q(x), and r(x) denote the following open statements. p(x): x^2-8x+15=0; q(x): x is odd; r(x): x>0; Universe: Integers Determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample. 8a. For all x [p(x)->g(x)]:

Database System Concepts
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
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  1. Let p(x), q(x), and r(x) denote the following open statements. p(x): x^2-8x+15=0; q(x): x is odd; r(x): x>0; Universe: Integers

 

Determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample.

3. Let p(x), q(x), and r(x) denote the following open statements. p(x): x^2-8x+15=0; q(x): x is odd; r(x): x>0; Universe: Integers Determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample. 8a. For all x [p(x)->q(x)]:
Transcribed Image Text:3. Let p(x), q(x), and r(x) denote the following open statements. p(x): x^2-8x+15=0; q(x): x is odd; r(x): x>0; Universe: Integers Determine the truth or falsity of each of the following statements. If a statement is false, give a counterexample. 8a. For all x [p(x)->q(x)]:
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Step 1

Solution-:

 

Given,

          We have from given question-: p(x) => x2 -8x +15=0  

                                                             q(x)=> x is odd

                                                             r(x)=> x>0        

 

Now we will try to factorize p(x)=>  x2 -8x +15=0  

                                                   => (x-3)*(x-5)=0

                                                   => x-3=0 or x-5=0

                                                   => x=3 or x=5  ---------------------------------------------------->(1)

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