The problem states that $P$ and $Q$ are subsets of a universal set. We need to find the value of $(P \cup Q) \cap Q$.

1. Problem Description

The problem states that $P$ and $Q$ are subsets of a universal set. We need to find the value of $(P \cup Q) \cap Q$.

2. Solution Steps

We can use the distributive property of sets. However, a simpler approach is to use the absorption law.

We are given $(P \cup Q) \cap Q$.

$A \cap (A \cup B) = A$

$A \cup (A \cap B) = A$

Let $A = Q$ and $B = P$.

$(P \cup Q) \cap Q = Q \cap (P \cup Q)$

By the commutative property of union, $P \cup Q = Q \cup P$.

Therefore, $Q \cap (P \cup Q) = Q \cap (Q \cup P)$.

Using the absorption law: $A \cap (A \cup B) = A$, we have

$Q \cap (Q \cup P) = Q$.

Alternatively:

The union of P and Q, $P \cup Q$, contains all elements in P as well as all elements in Q. The intersection of this union with Q, $(P \cup Q) \cap Q$, would contain all elements that are in both $(P \cup Q)$ and Q. Since all elements in Q are already in $(P \cup Q)$, the intersection is simply Q.

3. Final Answer

Q