Kripke models - prove that formula is not tautology in intuitionistical logic

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My teacher proved that following formula is not tautology in intuitionistical logic:
$$\neg(p\wedge q)\Leftrightarrow (\neg p\vee\neg q)$$
Is it sufficient to show (and we try to do it) that $$\neg(p\wedge q)\Rightarrow (\neg p\vee\neg q)$$ is not tautology.
My teacher wrote red and black formulas. My formulas are green - there are formulas that to my eye my teacher forgot to write.
I know that teacher give arbitrar Kripke model. Tell me please:
1. If my green "supplement" is correct ?
2. From what my teacher conclude red formulas ? When it comes to black things I know that it is about kripke model.
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