Answer
a) $r\wedge \neg p$
b)$\neg p \wedge q\wedge r$
c)$(r\Rightarrow q)\Leftrightarrow \neg p$
d)$\neg q\wedge \neg p\wedge \ r$
e)$(q \Rightarrow \neg r\wedge \neg p)\wedge\neg(\neg r\wedge \neg p\Rightarrow q)$
f) $(p\wedge r)\Rightarrow \neg q$
Work Step by Step
Represent each connection between propositions, labelled using $p, q, r$ as defined, and remember that "but" does not show a form of implication or connection other than $a \wedge \neg b$.
