Exercise B

Use truth tables to determine whether these sentences are jointly satisfiable, or jointly unsatisfiable:

1. $A\rightarrow A$, $\neg A\rightarrow\neg A$, $A\wedge A$, $A\vee A$

2. $A\vee B$, $A\rightarrow C$, $B\rightarrow C$

3. $B\wedge(C\vee A)$, $A\rightarrow B$, $\neg(B\vee C)$

4. $A\leftrightarrow(B\vee C)$, $C\rightarrow\neg A$, $A\rightarrow\neg B$