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Let p, q, and r be the propositions
p : You have the flu.
q : You miss the final examination.
r : You pass the course.
Express each of these propositions as an English sentence.

  1. $p \rightarrow q$
  2. $\neg q \leftrightarrow r$
  3. $q \rightarrow \neg r$
  4. $p \vee q \vee r$
  5. $(p \rightarrow \neg r) \vee (q \rightarrow \neg r)$
  6. $(p \wedge q) \vee (\neg q \wedge r)$
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a. If you have the flu then you will miss the final examination.
b. You will pass the course if and only if you don't miss the final examination.
c. If you miss the final examination then you will not pass the course.
d. You have the flu or y
ou miss the final examination or you pass the course.
e. if you have the flu then you will not pass that course or if you miss the final examination then you will not pass that course.
f. If you have the flu and  you miss the final examination or you don't miss the final examination and pass the course.
 

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