boolean - How to simplify this propositional logic expression (DNF)? -

i simplified original problem point

((p∧¬r)∨(¬q∨r))∧((q∧¬r)∨(¬p∨r))

, , got stuck here. next step? help!!

i solving you.

hint-1: ((p∧q)∨r) = (pvr) ∧ (qvr)

hint-2: p ∧ true = p

hint-3: p v true = true

answer

it true in end. check once.

next step be

= [(p v (~q v r)) ^ ( ~r v (~q v r))]  ^[(q v (~p v r)) ^ ( ~r v (~p v r))]  = (p v ~q v r) ^ ( ~p v q v r) = r v (  (p v ~q) ^ ( q v ~p)) = r v ((  q -> p ) ^ ( p -> q))    = r v (p <-> q) 

whenever r true true. else

  p  q   p<->q ------------------    f f      t    f t      f    t f      f    t t      t 

so conforms truth table. shown above trincot.