I've got the following question regarding Disjunctive Normal Form: Exercise
I've got answers for both of the questions and just want to check if they are correct
For the first part, the answer that I got is:
$$\begin{align} α(P,Q,R) \iff &(P \wedge Q \wedge Q) \vee (P \wedge \neg Q \wedge R) \vee (P \wedge \neg Q \wedge \neg R) \vee (¬ P \wedge Q \wedge R)\\ &\vee (¬ P \wedge Q \wedge ¬ R) \vee (¬ P \wedge ¬ Q \wedge R) \vee (¬ P \wedge ¬ Q \wedge ¬ R)\end{align}$$
For the second part, which is to write a more compact Boolean expression for the predicate α(P,Q,R) with the truth table in the image, I got:
$$α(P,Q,R) \iff ¬ (¬ P \wedge ¬ Q \wedge R) $$
I'm more sure about the first one over the second one, but i'd be grateful if anyone would be able to see if they get the same answers and see if i've gone wrong somewhere.