Exercise G

Determine whether each collection of sentences is jointly satisfiable or jointly unsatisfiable. Justify your answer with a complete or partial truth table as appropriate.

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

2. $A\rightarrow\neg A$, $\neg A\rightarrow A$

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

4. $A\vee B$, $A\rightarrow C$, $B\rightarrow C$, $\neg C$

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

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

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

8. $A\leftrightarrow B$, $\neg B\vee\neg A$, $A\rightarrow B$

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

10. $\neg(A\wedge\neg B)$, $B\rightarrow\neg A$, $\neg B$