# How to solve: Show that a formula is PL-valid if and only if it is LP-valid [closed]

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

• What is PL ? Prop logic ? and LP ? – Mauro ALLEGRANZA Feb 19 at 7:00
• It seems that you are working with three-valued logics. there are many... – Mauro ALLEGRANZA Feb 19 at 9:01
• I suggest you re-ask this on Mathematics (with the same tags). They will be more likely able to help you with a symbolic derivation/proof. – Mitch Feb 20 at 17:32
• If the answer below is enough for you, please accept it and we can "close" the post. – Mauro ALLEGRANZA Feb 21 at 10:24