Discrete mathematics & its applications with combinatorics and graph theory-kenneth H rosen

Question

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. 

How can I write these propositions using p, q, and r and logical connectives? 

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

b.) You get an A on the final, you do every excercise 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 excercise in this book; nevertheless, you get an A in this class. 

e.) Getting an A on the final and doing every excersise 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 excercise in this book or you get an A on the final.

Comments

thank you :)

Answer 1

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

 r ∧ ~q

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

p ∧ q ∧ r

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

r $\rightarrow$ p

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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.

p ∧ ~ q ∧ r 

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

( p ∧ q ) $\rightarrow$ r

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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.

r ↔ ( q ∨ p )

Comments

I did not get c option  rest is fine .

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what you didn't get?

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the staement in the C is a little clever representation.. In simple way,if you get A in the Final then only it is possible to get A in the class,

So A in final implies A in class

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No. Option C is r implies p. That is if you get an A in the class it implies you have got an A in final. But you can get an A in final and still not get an A in class as the given condition is necessary but not sufficient.