Exercise A

Use complete or partial truth tables (as appropriate) to determine whether these pairs of sentences are logically equivalent:

1. $A$, $\neg A$

2. $A$, $A\vee A$

3. $A\rightarrow A$, $A\leftrightarrow A$

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

5. $A\wedge\neg A$, $\neg B\leftrightarrow B$

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

7. $\neg(A\rightarrow B)$, $\neg A\rightarrow\neg B$

8. $(A\rightarrow B)$, $(\neg B\rightarrow\neg A)$