Let's express each of these propositions using the symbols $p$ (you get an A on the final exam), $q$ (you did every exercise in this book), and $r$ (you get an A in this class), along with logical connectives.

a) You get an A in this class but did not do every exercise in this book.

This can be expressed as: $r \land \neg q$

b) You get an A on the final, do every exercise in this book, and get an A in this class.

This can be expressed as: $p \land q \land r$

c) To get an A in this class, it is necessary for you to get an A on the final.

This can be expressed as: $r \rightarrow p$

d) You get an A on the final but did not do every exercise in this book; nevertheless, you get an A in this class.

This can be expressed as: $p \land \neg q \land r$

e) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.

This can be expressed as: $(p \land q) \rightarrow r$

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Do you want details on any of these logical expressions, or do you have any questions?

Here are five questions that extend these concepts:

1. How do we represent the logical expression for "If you did every exercise in the book, then you get an A on the final"?
2. What is the contrapositive of the expression $r \rightarrow p$?
3. How would you express "Getting an A in this class is sufficient for getting an A on the final and doing every exercise"?
4. How can we represent "You did not get an A on the final and did every exercise in this book"?
5. What is the converse of the statement $(p \land q) \rightarrow r$?

Tip: When working with logical connectives, understanding the difference between "necessary" and "sufficient" conditions is crucial for accurate translation into logical expressions.