propositions

[logistic_guy]

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

$\displaystyle \bold{a)}$ You get an A in this class, but you do not do every exercise in this book.
$\displaystyle \bold{b)}$ You get an A on the final, you do every exercise in this book, and you get an A in this class.
$\displaystyle \bold{c)}$ To get an A in this class, it is necessary for you to get an A on the final.
$\displaystyle \bold{d)}$ 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.
$\displaystyle \bold{e)}$ Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.
$\displaystyle \bold{f)}$ 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.

 

[logistic_guy]

$\displaystyle \bold{a)}$ You get an A in this class, but you do not do every exercise in this book.

$\displaystyle r \land \overline{q}$

 

[logistic_guy]

$\displaystyle \bold{b)}$ You get an A on the final, you do every exercise in this book, and you get an A in this class.

$\displaystyle p \land q \land r$

 

[logistic_guy]

$\displaystyle \bold{c)}$ To get an A in this class, it is necessary for you to get an A on the final.

$\displaystyle r \rightarrow p$

 

[logistic_guy]

$\displaystyle \bold{d)}$ 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.

$\displaystyle p \land \overline{q} \land r$

 

[logistic_guy]

$\displaystyle \bold{e)}$ Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.

$\displaystyle (p \land q) \rightarrow r$

 

[logistic_guy]

$\displaystyle \bold{f)}$ 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.

$\displaystyle r \leftrightarrow (q \lor p)$