I'm trying to determine whether there exists a model for the following logical formula: $(p_1 \to (p_2 \lor p_3)) \land(p_2 \to \neg p_3) \land ((p_1 \lor p_3) \to \neg p_2)$. Here's my understanding of the formula: If p1 is true, then either p2 or p3 must be true, and if p2 is true, then p3 must be false. However, this seems to create a conflict because if p1 is true, p2 cannot be false. Can anyone confirm whether a model exists for this formula or explain why it might not be possible? Thank you!