Prove that formula is not tautology.
Show Kripke's model proving that the following formula isn't tautology in intuitionistic logic. $ \neg ( p \wedge q ) \implies (\neg p \vee \neg q) $
Please help/hint me ;)
I think that a simple three-nodes model with $w_0$ as vertex and $w_1$ and $w_2$ as leaves [i.e. $w_i \ge w_0, i=1,2$] where :
no atom is forced by $w_0$
and :
$w_1 \Vdash p \ $ , $ \ w_2 \Vdash q$
will suffice.
We have $w_0 \Vdash \lnot (p \land q)$ because for all $w_i \ge w_0 : w_i \nVdash (p \land q)$.
But $w_1 \nVdash \lnot p$ and $w_2 \nVdash \lnot q$.