Trying to understand how to simplify more complex formula's, for example
$ \lnot ([(\lnotπ \lor π) \land (\lnotπ \land π \land π)] \lor \lnotπ)$
I've started with this:
$= Β¬ [(Β¬π β¨ π) β§ (Β¬π β§ π β§ π)] ⧠¬¬π $ (de Morgans Law)
$= Β¬ [(Β¬π β¨ π) β§ (Β¬π β§ π β§ π)] β§ π $ (double negation)
$= (Β¬ (Β¬π β¨ π) β¨ Β¬ (Β¬π β§ π β§ π)) β§ π$ (de Morgans law)
$= ((¬¬π β§ Β¬π) β¨ (¬¬π β¨ Β¬π β¨ Β¬π)) β§ π $ (de Morgans law)
$= ((π β§ Β¬π) β¨ (π β¨ Β¬π β¨ Β¬π)) β§ π$ (double negation)
$= ((π β§ Β¬π) β§ π) β¨ ((π β¨ Β¬π β¨ Β¬π) β§ π )$ (Distributive)
$= ((π β§ Β¬π) β§ π) β¨ (π β§ π) β¨ (Β¬π β§ π ) β¨ (Β¬π β§ π ) $ (Distributive)
However I think I'm going down the wrong track and would appreciate some help. Thanks