Math Logic

Don't remember the name, but:

p ^ (~p v q) = p ^ q
~(p^(~p v q)) = ~(p ^ q)
~p v (p ^ ~q) = ~p v ~q

=/ assuming that's a property, we weren't taught that, closest is absorption (p ^ (p v q) = p), do you think there's another way of doing it? otherwise the professor told us to do something we can't do yet...

Edit:
Thanks for that

~[ (p^~p) v (p^q)] v q by distributivity law
~[ 0 v (p^q)] v q

I left it there and then took the ~ to get to:

1 v ~(p^q) v q
1 v q
1

ok now, here I don't even know what I have to do: (asked to deny.. but what does that even mean)

( x ) [p(x) ^q(x)] => (x)[p(x) v q(x)]