Answer to Question #163809 in Discrete Mathematics for Zhang Xi

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. Write these propositions using p, q, and r and logical connectives (including negations). Then, Construct the truth table of the each proposition 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, but you do every exercise in this book, and you get an A in this class. c) 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. 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.

Answer 1

Given,

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

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

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

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

$\Rightarrow r ∧¬ q$

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

$\Rightarrow p ∧q ∧r$

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

 $\Rightarrow r →p$

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.

 $\Rightarrow p ∧¬ q ∧r$

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

 $\Rightarrow (p ∧q) → r$

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.

$\Rightarrow r ↔ (p ∨q)$