Duality discrete math problem This is the only answer I got wrong on my HW and the prof does not want to give us the correct answers before our midterm

The dual of a compound proposition that contains only the logical operators $\lor$ , $\land$ , and
  $\neg$ is the compound proposition obtained by replacing each $\lor$ by $\land$ , each $\land$ by $\lor$ , each $\def\T{{\rm T}}\def\F{{\rm F}}$
  $\T$ by $\F$ , and each $\F$ by $\T$ . The dual of $s$ is denoted by $s^*$. Find the dual of these compound propositions.
a) $p \lor\neg q$  

I got $\neg p \land q$  

b) $p \land (q \lor (r \land \T))$  

My answer was $\neg p \lor (\neg q \land r)$  

c) $(p \land \neg q) \lor (q \land \F)$  

My answer was $(\neg p \lor q) \land  \neg q$
I have tried googling the problem and cannot come up with anything on duals and our lectures are online and upon reviewing do not see anything. I am just confused and looking for a little guidance on what was incorrect with my answers.

You did more as you should. Forming the dual just wants you to replace $p$ by $\neg p$ for each literal $p$, $\lor$ by $\land$ and vice versa and $T$ by $F$. You did more than that, in dualising (2), one obtains 
$$ \neg p \lor \bigl( \neg q \land (\neg r \lor F)\bigr) $$
(you missed a $\neg$ in front of $r$). We have of course $\neg r \lor F \equiv \neg r$, but this is not part of dualising. Same for (3), the dual proposition is 
$$ (\neg p \lor q) \land (\neg q \lor T)$$
