The problem asks to determine the result of various set operations involving sets $P$, $Q$, and $R$. Let's go through them step by step.

The sets given are:

• $P = \{1, 2, 3\}$
• $Q = \{3, 4, 5, 6\}$
• $R = \{6, 7, 8\}$

(a) $P \cup (Q \cap R)$

• First, calculate $Q \cap R$: the intersection of $Q$ and $R$ is the elements that are in both sets. $Q \cap R = \{6\}$.
• Then, calculate $P \cup (Q \cap R)$: the union of $P$ and $\{6\}$ is $\{1, 2, 3, 6\}$.

So, the result for (a) is $\{1, 2, 3, 6\}$.

(b) $(P \cup Q) \cap (P \cup R)$

• First, calculate $P \cup Q$: the union of $P$ and $Q$ is $\{1, 2, 3, 4, 5, 6\}$.
• Then, calculate $P \cup R$: the union of $P$ and $R$ is $\{1, 2, 3, 6, 7, 8\}$.
• Now, calculate $(P \cup Q) \cap (P \cup R)$: the intersection of these two sets is $\{1, 2, 3, 6\}$.

So, the result for (b) is $\{1, 2, 3, 6\}$.

(c) $P \cap (Q \cup R)$

• First, calculate $Q \cup R$: the union of $Q$ and $R$ is ( {