Is the following a tautology?

Nov 2011
90
0
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!
 

Plato

MHF Helper
Aug 2006
22,507
8,664
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 \(\displaystyle \neg r \vee \left( {\neg q \vee p} \right)\)