Prove, or find a counterexample to, each of the following assertions:
-
If
$\alpha\models\gamma$ or$\beta\models\gamma$ (or both) then$(\alpha\land \beta)\models\gamma$ -
If
$(\alpha\land \beta)\models\gamma$ then$\alpha\models\gamma$ or$\beta\models\gamma$ (or both). -
If
$\alpha\models (\beta \lor \gamma)$ then$\alpha \models \beta$ or$\alpha \models \gamma$ (or both).