Verify by constructing truth tables that the following wffs are tautologies. Note that the tautologies in parts \(\mathrm{b}, \mathrm{e}, \mathrm{f}\), and \(\mathrm{g}\) produce equivalences such as \(\left(A^{\prime}\right)^{\prime} \Leftrightarrow A\).
a. \(A \vee A^{\prime}\)
b. \(\left(A^{\prime}\right)^{\prime} \leftrightarrow A\)
c. \(A \wedge B \rightarrow B\)
d. \(A \rightarrow A \vee B\)
e. \((A \vee B)^{\prime} \leftrightarrow A^{\prime} \wedge B^{\prime} \quad\) (De Morgan's law)
f. \((A \wedge B)^{\prime} \leftrightarrow A^{\prime} \vee B^{\prime} \quad\) (De Morgan's law)
g. \(A \vee A \leftrightarrow A\)