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Your class has a textbook and a final exam. Let $P,Q$ and $R$ be the following propositions:

  • $P:$ You get an $A$ on the final exam.
  • $Q:$ You do every exercise in the book.
  • $R:$ You get an $A$ in the class.

Translate the following assertions into propositional formulas using $P,Q,R$ and the propositional connectives $\bigwedge$ (and), $\bigvee$ (or),$\neg$ (not) and $\Rightarrow$(implies).

  1. To get an $A$ in the class, it is necessary for you to get an $A$ on the final.
  1. 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.
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