I don't really understand this problem, but I'm going to spill out what I've taken notes on. I know that in order to solve this we would need to use the contrapositive in each direction.
I'm going to use 'a' in place of phi
So we want to show that a is PL valid iff a is LP valid.
I think the next thing to do is assume a is not LP valid - I would also use Kleene's valuation function: there is a trivalent I, KVI(a)=0
In order to show a is not LP valid, I think we would need to prove that vi(a)=0 and KVi(a)=0.
To be honest, I don't know exactly what direction to take this. From class, we were told the crucial aspect was to prove Vi(a)=0 and KVi(a)=0