Exercise I

Determine whether each argument is valid or invalid. Justify your answer with a complete or partial truth table as appropriate.

1. $A\leftrightarrow\neg(B\leftrightarrow A)\therefore A$

2. $A\vee B$, $B\vee C$, $\neg A\therefore B\wedge C$

3. $A\rightarrow C$, $E\rightarrow(D\vee B)$, $B\rightarrow\neg D\therefore(A\vee C)\vee(B\rightarrow(E\wedge D))$

4. $A\vee B$, $C\rightarrow A$, $C\rightarrow B\therefore A\rightarrow(B\rightarrow C)$

5. $A\rightarrow B$, $\neg B\vee A\therefore A\leftrightarrow B$