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