1. ## Disjunctive Normal Form

I have a question here requiring logical equivalences.

Express (not(p v q)) ^ r in disjunctive normal form by applying logical equivalences.

I must use logical equivalences to complete it, I cant construct a truth table.

from the laws i know associativity says ((p v q) v r) <==> (p v (q v r)).
and with distributivity i have (p v (q ^ r) <==> ((p v q) ^ (p v r))

I feel like these are the laws I need to solve the problem but I just cannot seem to wrap my head around it. Can somebody please put me on the right track. Thanks.

2. i will assume (not(p v q)) ^ r means ~(P\/Q)/\R
so what you want to do first is bring the ~ in as so:
(~P/\~Q)/\R
then you want to bring the R into the (~P/\~Q) as so:
(~P/\R)\/(~Q/\R)
so now you have the correct form for a DNF, but do not have all the propositional variables in each OR'd section. So now add a Q to the first section and a P to the second one as so:
(~P/\Q/\R)\/(~P/\~Q/\R)\/(P/\~Q/\R)\/(~P/\~Q/\R)
and you're done.

hope this helps (i know i'm a bit late, but this is my first time on this forum and i found your question through google)