Question

Let q, r, p 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 the class Write the following propositions using p, q, and r and logical connectives a) You get an A in this class, but you do not do every exercise in the book b) You get an A on the final, you do every exercise 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 exam 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 e) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class. f) You 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. g) It is either you get an A on the final exam or you get A in the class ,but you get an A on the final exam if you do every exercise in the book

          Let q, r, p 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 the class
Write the following propositions using p, q, and r and logical connectives
a) You get an A in this class, but you do not do every exercise in the book
b) You get an A on the final, you do every exercise 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 exam
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
e) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.
f) You 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.
g) It is either you get an A on the final exam or you get A in the class ,but you get an A on the final exam if you do every exercise in the book

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Let q, r, p 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 the class
Write the following propositions using p, q, and r and logical connectives
a) You get an A in this class, but you do not do every exercise in the book
b) You get an A on the final, you do every exercise 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 exam
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
e) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.
f) You 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.
g) It is either you get an A on the final exam or you get A in the class ,but you get an A on the final exam if you do every exercise in the book

Added by Jennifer B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Eleni Katirtzoglou

06/04/2022

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- \( q \): You do every exercise in this book. - \( r \): You get an A in the class. Show more…

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Let q, r, p 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 the class Write the following propositions using p, q, and r and logical connectives a) You get an A in this class, but you do not do every exercise in the book b) You get an A on the final, you do every exercise 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 exam 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 e) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class. f) You 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. g) It is either you get an A on the final exam or you get A in the class ,but you get an A on the final exam if you do every exercise in the book

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Transcript

00:02 Hi, here we have a problem in logic.

00:04 We are given three propositions, qr p.

00:08 P is you get an a on the final exam, q is you do every exercise in this book, and r is you get an a in the class.

00:16 And we are asked to use these three propositions and write the composite propositions that follow here using p, qr and logical connectives.

00:27 Before we start, let's just class.

00:29 Clarify what it means sufficient and necessary conditions if we have if x then y then y is a necessary condition for x and x is a sufficient condition for y okay so now let's start with the problems we have the first proposition is you get a in the class so that means we have here r but you do not do every exercise in the book you do not do every exercise in the book this is actually not let me just use not q and the connective that the word that connects these two together is the word but but it's the same as and so what we have here is we have r and not q so this is the answer for a.

01:29 All right so now let's do b.

01:34 In b we have you get a name the final that means we get the name the final this is p you do every exercise in this book do every exercise in this book is q and then we have and you get an a in the class and we have r so all of these things are actually connected with and so the proposition we have is p and q and r.

02:05 Okay, now part c.

02:08 To get an a in the class, so we have here p.

02:15 Sorry, this is p here.

02:17 To get an a in the class, it is necessary for you to get an a in the final exam.

02:26 And we have r.

02:27 So what is the necessary condition here? it is necessary to get an a on the final exam.

02:39 Sorry, i get confused a little bit with what is p and what is r.

02:43 Let me start this thing again.

02:47 So we have, it is necessary for you to get an a on the final exam, to get an a in the class...

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