Prove that p (p q) is a tautology using a truth table.

We need columns for $p$, $q$, $\neg p$, $p \to q$, and $\neg p \to (p \to q)$.

Recall that $p \to r$ is false only when $p$ is true and $r$ is false; otherwise, it is true.

All the truth values in the column for $\neg p \to (p \to q)$ are 'T' (True).

Since the expression $\neg p \to (p \to q)$ is true for all possible truth values of $p$ and $q$, it is a tautology.