Yes! Let’s compute the attribute closure of $P^+$ step by step for the given functional dependencies.

Problem setup:

• Relation $R(P, Q, X, Y, Z)$
• Functional dependencies:
  1. $PQ \rightarrow X$
  2. $P \rightarrow Y$
  3. $Y \rightarrow Z$
  4. $PX \rightarrow Q$

We are computing $P^+$, the attribute closure of $P$.

Steps to compute $P^+$:

1. Start with the attribute set: $P^+ = \{ P \}$.

2. Apply functional dependencies:

   • From $P \rightarrow Y$, we can add $Y$ to $P^+$.
     So, $P^+ = \{ P, Y \}$.

   • From $Y \rightarrow Z$, we can add $Z$ to $P^+$.
     Now, $P^+ = \{ P, Y, Z \}$.

3. Check other functional dependencies:

   • None of the remaining functional dependencies ($PQ \rightarrow X$ and $PX \rightarrow Q$) can be applied because we do not have $Q$ or $X$ in $P^+$ yet.

4. Stop when no new attributes can be added.

Final closure:

$P^+ = \{ P, Y, Z \}$.

Would you like detailed explanations for other closures (e.g., $XY^+$, $PQ^+$) or help with related concepts?

Here are 5 follow-up questions:

1. What is the purpose of attribute closures in database normalization?
2. How do you use closures to check if a set of attributes is a superkey?
3. Can you explain how functional dependencies determine closures?
4. How would the closure of $Q^+$ be computed, and why does it only include $Q$?
5. What changes in closures if we add another functional dependency?

Tip: Attribute closure is a key tool for determining keys and decomposing relations in higher normal forms!