[Math] Finding the principal disjunctive normal form (PDNF) of a Boolean expression

Question

Find the principal disjunctive normal form (PDNF) of a Boolean expression
$$((p\wedge q) \rightarrow r)\vee((p\wedge q)\rightarrow \neg r).$$
I tried by expanding it but I am stuck with the expression
$(\neg p \vee \neg q \vee r) \vee (\neg p \vee \neg q \vee \neg r)$. I don't know how to convert them into min terms. Please help me.

Answer 1

Expression mentioned is a Tautology. $$((p.q) \rightarrow r)+((p.q)\rightarrow r')=((p'+q'+r)+(p'+q'+r'))=p'+q'+1 = 1$$ So PDNF corresponding to it is $$(p'.q'.r')+(p'.q'.r)+(p'.q.r')+(p'.q.r)+(p.q'.r')+(p.q'.r)+(p.q.r')+(p.q.r)$$