How to simplify this propositional logic expression (DNF)?

Question

I simplified the original problem up to this point

((P∧¬R)∨(¬Q∨R))∧((Q∧¬R)∨(¬P∨R))

, and I got stuck here. What would be the next step? Thanks for the help!!

Answer 1

I am solving it with you.

Hint-1: ((P∧Q)∨R) = (PVR) ∧ (QVR)

Hint-2: P ∧ True = P

Hint-3: P V True = True

Answer

It would be true in the end. Check it once.

Next step would 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 is True it is True. Else

  P  Q   P<->Q
------------------
   F F      T
   F T      F
   T F      F
   T T      T

So it conforms to the truth table. Shown above by trincot.