I want to find a statement form in relaxed disjunctive normal form that is logically equivalent to $\displaystyle ((p \to q) \wedge (q \to r))$.

The solution has to be $\displaystyle (((\neg p \wedge \neg q) \vee (\neg p \wedge r))\vee (q \wedge r))$. But I don't see how the got this answer.

I used a truth table, where I've marked with a * the rows where the statement is true:

by looking at those rows the disjunctive normal form is

$\displaystyle ((\neg p \wedge \neg q) \wedge \neg r) \vee ((\neg p \wedge \neg q) \wedge r) \vee ((\neg p \wedge q) \wedge r) \vee ((p \wedge q) \wedge r)$

So how did they get a different answer? How can we get the right answer using the table?