202110181002 SGT

interpretation	$p$	$q$	$p\to q$	$\neg p\vee q$
$v_0$	0	0	1	1
$v_1$	0	1	1	1
$v_2$	1	0	0	0
$v_3$	1	1	1	1

These two formulas are logically equivalent, so $p\to q\equiv \neg p\vee q$.

$\mathcal{I}$ is the set of all interpretations, $\mathcal{I}=\{v_0,v_1,v_2,v_3\}$

A model is cases where the interpretation is true.

$\mathrm{mod}(p\to q)=\{v_0,v_1,v_3\}$ are the interpretations that make $p\to q$ true.

$\mathrm{mod}(\neg A)=\mathcal{I}-\mathrm{mod}(A)$ $\mathrm{mod}(A\cup B)=\mathrm{mod}(A)\cup \mathrm{mod}(B)$ $\mathrm{mod}(A\cap B)=\mathrm{mod}(A)\cap \mathrm{mod}(B)$

$\mathrm{mod}(A\cup \neg A)=\mathcal{I}$ $\mathrm{mod}(A\cap \neg A)=\varnothing$

$v_0\models p\to q$

DNF = $\neg ,\wedge ,\vee$