Exercise G

Determine whether each collection of sentences is jointly satisfiable or jointly unsatisfiable using a complete truth table.

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

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

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

4. $A\rightarrow B$, $A\wedge\neg B$

5. $A\rightarrow(B\rightarrow C)$, $(A\rightarrow B)\rightarrow C$, $A\rightarrow C$