Exercise E

Determine whether each sentence is a tautology, a contradiction, or a contingent sentence. Justify your answer with a complete or partial truth table as appropriate.

1. $\neg(A\vee A)$

2. $(A\rightarrow B)\vee(B\rightarrow A)$

3. $[(A\rightarrow B)\rightarrow A]\rightarrow A$

4. $\neg[(A\rightarrow B)\vee(B\rightarrow A)]$

5. $(A\wedge B)\vee(A\vee B)$

6. $\neg(A\wedge B)\leftrightarrow A$

7. $A\rightarrow(B\vee C)$

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

9. $(B\wedge D)\leftrightarrow[A\leftrightarrow(A\vee C)]$

10. $\neg[(A\rightarrow B)\vee(C\rightarrow D)]$