Answer
a) $p \land \neg q$
b) $p \lor (q \land (r \lor F)$
c) $(p \lor \neg q) \land (q \lor T)$
Work Step by Step
The dual operator replaces $\lor$ by $\land $, $\land$ by $\lor$ , T by F and F by T.
a) given: p $\lor$ $\neg$q
Replace $\lor$ by $\land$
$$p \land \neg q$$
b)given: $p \land (q \lor (r \land T)$
Replace $\lor$ by $\land $, $\land$ by $\lor$ , T by F and F by T
$$p \lor (q \land (r \lor F)$$
c)given: $(p \land \neg q) \lor (q \land F)$
Replace $\lor$ by $\land $, $\land$ by $\lor$ , T by F and F by T
$$(p \lor \neg q) \land (q \lor T)$$
