2 votes

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.

1 vote

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

r ∧ ~q

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

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

r $\rightarrow$ p

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

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

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 )