Aritificial Intelligence: A Modern Approach

Exercise 7.8

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 $\alpha\models (\beta \land \gamma)$ then $\alpha \models \beta$ and $\alpha \models \gamma$.

3. If $\alpha\models (\beta \lor \gamma)$ then $\alpha \models \beta$ or $\alpha \models \gamma$ (or both).