Let p, q and r be the propositions such that, p: “You get an A on the final exam
ID: 3011406 • Letter: L
Question
Let p, q and r be the propositions such that,
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 the following propositions using p, q, r and logical connectives.
(a) If you do every exercise in this book then you will get an A in this class.
(b) You get an A in class only if you get an A in the final exam.
(c) To get an A in this class it is necessary for you to get an A in the final.
(d) Getting an A in the final and doing every exercise in this book is sufficient for getting an A in this class.
(e) 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 exam.
Explanation / Answer
(a) If you do every exercise in this book then you will get an A in this class. q r (b) You get an A in class only if you get an A in the final exam. r p (c) To get an A in this class it is necessary for you to get an A in the final. p r (d) Getting an A in the final and doing every exercise in this book is sufficient for getting an A in this class. (p q) r (e) 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 exam. r (p q)
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