Step-by-step Solution:

We need to simplify the given set expression: \[ (P - Q) \cup (Q - P) \cup (P \cap Q) \] Step 1: Understanding Each Term \[\] \( P - Q \) (i.e., \( P \setminus Q \)) consists of elements in \( P \) but not in \( Q \). \[\] \( Q - P \) (i.e., \( Q \setminus P \)) consists of elements in \( Q \) but not in \( P \). \[\] \( P \cap Q \) consists of elements common to both \( P \) and \( Q \). \[\] Step 2: Rewriting in Terms of Union \[\] The three parts together cover: \[\] All elements in \( P \) that are not in \( Q \) (\( P - Q \)) \[\] All elements in \( Q \) that are not in \( P \) (\( Q - P \)) \[\] All elements that are in both \( P \) and \( Q \) (\( P \cap Q \)) \[\] Thus, their union forms: \[ (P - Q) \cup (Q - P) \cup (P \cap Q) = P \cup Q \] Conclusion \[\] The given set expression simplifies to: \( P \cup Q \)