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Let p and q be the propositionsp : I bought a lottery

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 8E Chapter 1.1

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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1
Problem 8E

Let \(p\) and \(q\) be the propositions

\(p:\) I bought a lottery ticket this week.

\(q\) : I won the million dollar jackpot.

Express each of these propositions as an English sentence.

a) \(\neg p\)

b) \(p \vee q\)

c) \(p \rightarrow q\)

d) \(p \wedge q\)

e) \(p \leftrightarrow q\)

f) \(\neg p \rightarrow \neg q\)

g) \(\neg p \wedge \neg q\)

h) \(\neg p \vee(p \wedge q)\)

Equation Transcription:

                

        

                

                

        

        

        

Text Transcription:

p  

q  

Neg p

P vee q        

p rightarrow q                

p wedge q                                  

p leftrightarrow  q  

p rightarrow q                  

Nega p rightarrow neg q  

Nega p wedge neg q            

Nega p vee (p wedge q)

Step-by-Step Solution:
Step 1 of 3

Solution:

Step1

Given that

I bought a lottery ticket this week  and I won the million dollar jackpot be a preposition p and q.

Step2

To find

Express each of these propositions as an English sentence.

Step3

From the given proposition we are finding that

a.  

This means this week i have not buy a lottery ticket.

Step4

b.   

This means this week either i bought a lottery ticket or i won the million dollar jackpot.

Step5

c.  

This means this week if i bought a lottery ticket then the million dollar jackpot i won.

Step6

d.

This means this week if i bought a lottery ticket and the million dollar jackpot i won.

Step7

e.

This means this week if i bought a lottery ticket  if and only if the million dollar jackpot i won.

Step8

f.

This means this week if i  have not bought a lottery ticket then the million dollar jackpot i have not won.

Step9

g.

This means this week if i  have not bought a lottery ticket and the million dollar jackpot i have not won.

Step10

h.

This means either this week i have not bought a lottery ticket or else i have and the million dollar jackpot i  won.

Step 2 of 3

Chapter 1.1, Problem 8E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

The full step-by-step solution to problem: 8E from chapter: 1.1 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 8E from 1.1 chapter was answered, more than 540 students have viewed the full step-by-step answer. This full solution covers the following key subjects: propositions, million, english, express, jackpot. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “?Let \(p\) and \(q\) be the propositions\(p:\) I bought a lottery ticket this week.\(q\) : I won the million dollar jackpot.Express each of these propositions as an English sentence.a) \(\neg p\)b) \(p \vee q\)c) \(p \rightarrow q\)d) \(p \wedge q\)e) \(p \leftrightarrow q\)f) \(\neg p \rightarrow \neg q\)g) \(\neg p \wedge \neg q\)h) \(\neg p \vee(p \wedge q)\)Equation Transcription: Text Transcription:p q Neg p P vee q p rightarrow q p wedge q p leftrightarrow q p rightarrow q Nega p rightarrow neg q Nega p wedge neg q Nega p vee (p wedge q)” is broken down into a number of easy to follow steps, and 95 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

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Let p and q be the propositionsp : I bought a lottery