To find $|P \cup Q|$, we need to calculate the size of the union of the sets $P$ and $Q$. The union of two sets includes all unique elements from both sets.

Given:

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

Step 1: List all elements in $P \cup Q$

Union includes all distinct elements: $P \cup Q = \{b, l, u, e, p, r, y\}$

Step 2: Count the number of unique elements

The unique elements are $\{b, l, u, e, p, r, y\}$, which is a total of 7 elements.

Final Answer:

$|P \cup Q| = 7$

Would you like a detailed breakdown of how I determined the unique elements?

Related Questions:

1. What is $|P \cap Q|$, the size of the intersection of $P$ and $Q$?
2. How do you calculate the union of more than two sets?
3. What is the difference between the union and the intersection of two sets?
4. Can you visualize the union operation using a Venn diagram?
5. How would the answer change if $U$ were a smaller finite universal set?

Tip:

When calculating unions, always check for duplicates to avoid over-counting elements.