# Is the following a tautology?

• Oct 29th 2012, 08:18 AM
Nora314
Is the following a tautology?
Hi everyone!

On my exam there is always a question like this:

Is the following a tautology:

[(r -> q) -> p] ↔ [r -> (q -> p)]

I know how to solve this pretty easy by using a truth table or by just thinking a bit about the logic behind the statement. I was just wondering, is there some easier way to do this? I know about logical equivalence identities, but I find them difficult to apply to these kind of problems.

Thanks to anyone who reads this!
• Oct 29th 2012, 08:46 AM
Plato
Re: Is the following a tautology?
Quote:

Originally Posted by Nora314
Hi everyone!
Is the following a tautology:
[(r -> q) -> p] ↔ [r -> (q -> p)]

Say $r\equiv F,~q\equiv T,~\&~p\equiv F$. SO?

The first is $\neg \left( {\neg r \vee q} \right) \vee p$.

The second is $\neg r \vee \left( {\neg q \vee p} \right)$