Propositional Logic Discrete Maths: P => Q |- (P^Q) v (¬P^¬Q) v (¬P ^Q)

Question

I'm hard stuck I don't even know what assumption to take, I was thinking something of the following, maybe someone can help me in the right direction (P.S I can't use any lemmas only basics i.e. conjunction bi/implication disjunction negation introduction and elimination rules (i.e. cant use P^¬P |- Q or any other lemma), :

1) P=>Q
.
.
.
¬(P^Q) => ¬               (=> intro)
¬(P^Q) =>                 (=> intro)
¬¬(P^Q)                   (¬  intro)
(P^Q)                     (¬  elim)
(P^Q) v (¬P^¬Q) v (¬P ^Q) (v intro)

Thanks in advance!

Answer 1

Case P. Then P and Q.
Case not P.
. . Subcase not Q. Thus not P and not Q.
. . Subcase Q, Thus not P and Q.