6. 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. a) You get an A in this class, but you do not do every exercise in this book. b) To get an A in this class, it is necessary for you to get an A on the final. c) 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. d) 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.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. 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.
a) You get an A in this class, but you do not do every exercise in this book.
b) To get an A in this class, it is necessary for you to get an A on the final.
c)
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.
d) 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.
7. Determine whether the followings are true or false.
a) If 1 + 1 = 3, then 2 + 2 = 5.
b) If 1 + 1 =3, then cats can swim.
c) 1+1=2 if and only if 2 + 3 = 4.
d) 1+1=3 if and only if monkeys can fly.
8. For each of these sentences, determine whether an exclusive OR is intended. Explain your
answer.
a) Coffee or tea comes with dinner.
b) A password must have at least three digits or be at least eight characters long.
c) Experience with C++ or Java is required.
d) Lunch includes soup or salad.
Transcribed Image Text:6. 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. a) You get an A in this class, but you do not do every exercise in this book. b) To get an A in this class, it is necessary for you to get an A on the final. c) 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. d) 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. 7. Determine whether the followings are true or false. a) If 1 + 1 = 3, then 2 + 2 = 5. b) If 1 + 1 =3, then cats can swim. c) 1+1=2 if and only if 2 + 3 = 4. d) 1+1=3 if and only if monkeys can fly. 8. For each of these sentences, determine whether an exclusive OR is intended. Explain your answer. a) Coffee or tea comes with dinner. b) A password must have at least three digits or be at least eight characters long. c) Experience with C++ or Java is required. d) Lunch includes soup or salad.
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