Exercise D

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. $A\rightarrow\neg A$

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

3. $(A\rightarrow B)\leftrightarrow(B\rightarrow A)$

4. $A\rightarrow\neg(A\wedge(A\vee B))$

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

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

7. $[(A\wedge B)\wedge C]\rightarrow B$

8. $\neg\bigl[(C\vee A)\vee B\bigr]$

9. $\bigl[(A\wedge B)\wedge\neg(A\wedge B)\bigr]\wedge C$

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