First Order Logic - Consequence and Interpretation

Question

I'm trying to understand why this is false: $\varphi \vee \psi \models \chi \text{ iff } \varphi \models \chi \text{ or } \psi \models \chi.$

I think that the problem is that it can have two groups of interpretation and some doesn't hold for both. Any interpretation that shows why this is false will be very good accepted too. Thank you.

Answer 1

Hint: Take $\varphi$ to be True, $\psi$ to be False and $\chi$ to be False.

Answer 2

Do you see why this is true: $\varphi\vee\psi\models\chi$ iff $\varphi\models\chi$ and $\varphi\models\chi$?

Combined with what you thought should be true, we would have:
$\varphi\models\chi$ and $\varphi\models\chi$ iff $\varphi\models\chi$ or $\varphi\models\chi$. Do you think that should be true?

Suppose $\chi$ happens to be the same as $\varphi$. Do you think this is true:
$\varphi\vee\psi\models\varphi$ iff $\varphi\models\varphi$ or $\psi\models\varphi$?