I have been attempting to convent a prop to DNF using a group of common rules, i have applied them all but i think i should be able to get it smaller, This is what I've got so far. Thanks! $$(p \wedge (q \vee \neg p)) \rightarrow (q \wedge \neg (s \wedge r))$$ First, I remove the implication, as $p \rightarrow q$ is logically equivalent to $ \neg p \vee q$;
$$\neg (p \wedge (q \vee \neg p)) \vee (q \wedge \neg (s \wedge r))$$ Now I use the double negation rule to remove the extra nots
$$\neg (p \wedge (q \vee p)) \vee (q \wedge (s \wedge r))$$
Apply De Morgan's Laws
$$ (\neg p \wedge (q \vee p)) \wedge (\neg q \wedge (s \wedge r))$$ Use the distributive property to separate functions
$$ (\neg (p \wedge q) \vee (p \wedge p)) \wedge (\neg (q \wedge s) \vee (q \wedge r))$$
$p \wedge p$ is logically equivalent to $p$
$$ (\neg (p \wedge q) \vee (p)) \wedge (\neg (q \wedge s) \vee (q \wedge r))$$
Apply De Morgan's Laws some more
$$(\neg p \vee \neg q) \vee p) \wedge (\neg q \vee \neg s) \vee (\neg q \vee \neg r))$$