Rewrite: $\displaystyle (p \wedge (q \to (p \vee (p \wedge q)))) \wedge q$ and determine if its tautology, contradiction or neither. Using truth table I got neither.

My working out:

- $\displaystyle (p \wedge (q \to (p \vee (p \wedge q)))) \wedge q$

- $\displaystyle (p \wedge (q \to p)) \wedge q$

- $\displaystyle (p \wedge (\sim q \vee p)) \wedge q$

- $\displaystyle (p \wedge (p \vee \sim q)) \wedge q$

- $\displaystyle ((p \wedge p) \vee \sim q) \wedge q$

- $\displaystyle (p \vee \sim q) \wedge q$

Now im a little stuck. After the truth table, im assuming I have to finish off with just a "p". Any help would be much appreciated.