To solve $P \cup (Q \cap R)$ using the given sets:

Given Sets:

• $P = \{b, l, a, c, k\}$
• $Q = \{b, l, u, e\}$
• $R = \{p, u, r, e, l, y\}$

Steps:

1. Find $Q \cap R$:

   • Intersection ($\cap$) includes elements that are common in $Q$ and $R$.
   • Common elements between $Q = \{b, l, u, e\}$ and $R = \{p, u, r, e, l, y\}$ are: $Q \cap R = \{l, u, e\}.$

2. Union $P \cup (Q \cap R)$:

   • Union ($\cup$) includes all elements from both sets without duplication.
   • Combine $P = \{b, l, a, c, k\}$ and $Q \cap R = \{l, u, e\}$: $P \cup (Q \cap R) = \{b, l, a, c, k, u, e\}.$

Final Answer:

$P \cup (Q \cap R) = \{b, l, a, c, k, u, e\}.$

Would you like a detailed explanation of any specific step or concept?

Related Questions:

1. How do you compute the complement of a set?
2. Can you explain the difference between union and intersection in set theory?
3. How do subsets relate to intersections?
4. What are the practical applications of union and intersection in real-world problems?
5. Can you illustrate this problem using a Venn diagram?

Tip:

Always double-check the elements when performing intersections or unions to avoid overlooking shared or missing items.