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!

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

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

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