question.md

Prove each of the following assertions:

1. $\alpha$ is valid if and only if ${True}{\models}\alpha$.
   

2. For any $\alpha$, ${False}{\models}\alpha$.
   

3. $\alpha{\models}\beta$ if and only if the sentence $(\alpha {:;{\Rightarrow}:;}\beta)$ is valid.
   

4. $\alpha \equiv \beta$ if and only if the sentence $(\alpha{;;{\Leftrightarrow};;}\beta)$ is valid.
   

5. $\alpha{\models}\beta$ if and only if the sentence $(\alpha \land \lnot \beta)$ is unsatisfiable.