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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 1.1 - Problem 8e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 1.1 - Problem 8e

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# Let p and q be the propositionsp : I bought a lottery ISBN: 9780073383095 37

## Solution for problem 8E Chapter 1.1

Discrete Mathematics and Its Applications | 7th Edition

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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

Step 3 of 3

##### 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