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Q14P

Expert-verifiedFound in: Page 13

Book edition
7th

Author(s)
Kenneth H. Rosen

Pages
808 pages

ISBN
9780073383095

**Let p, q, and r be the propositions p : You get an A on the final exam. q : You do every exercise in this book. r : You get an A in this class. Write these propositions using p, q, and r and logical connectives (including negations). **

**a)You get an A in this class, but you do not do every exercise in this book.**

**b) You get an A on the final, you do every exercise in this book, and you get an A in this class. **

**c) To get an A in this class, it is necessary for you to get an A on the final.**

**d) You get an A on the final, but you don’t do every exercise in this book; nevertheless, you get an A in this class. **

**e) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class. f ) You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final.**

a) $r\wedge \neg q$

b) $p\wedge q\wedge r$

c) $r\to p$

d) $p\wedge \neg q\wedge r$

e) $(p\wedge q)\to r$

f) $r\leftrightarrow (p\vee q)$

**Proposition: 1. It is a declarative statement which can be either true or false. 2. It cannot be both true and false simultaneously**

*p*: You get an A on the final exam.

*q*: You do every exercise in this book.

*r*: You get an A in this class.

You get an A in this class, but you do not do every exercise in this book. The above given statement means $r\wedge \neg q$.

You get an A on the final, you do every exercise in this book, and you get an A in this class.

The given statement means $p\wedge q\wedge r$

To get an A in this class, it is necessary for you to get an A on the final.

The above given statement means $r\to p$

You get an A on the final, but you don’t do every exercise in this book; never the less, you get an A in this class

The given statement means $p\wedge \neg q\wedge r$.

Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.

The given statement means $(p\wedge q)\to r$.

You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final**.**

The given statement means $r\leftrightarrow (p\vee q)$

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