To find $|A \cup B|$, we use the principle of inclusion-exclusion:

$|A \cup B| = |A| + |B| - |A \cap B|$

Given values:

• $|A| = 8$
• $|B| = 5$
• $|A \cap B| = 3$

Substituting these values:

$|A \cup B| = 8 + 5 - 3 = 10$

Final Answer:

$\boxed{10}$

Would you like a breakdown of the principle of inclusion-exclusion?

Here are some related questions:

1. How do we calculate $|A \cup B \cup C|$ if a third set $C$ is included?
2. What happens if $A$ and $B$ are disjoint? How does $|A \cap B|$ affect the result?
3. How can we use Venn diagrams to visualize set operations?
4. If $|A| = x$, $|B| = y$, and $|A \cap B| = z$, how do we derive the formula?
5. Can this formula be extended to infinite sets?

Tip: Always check if two sets are disjoint before applying the formula—if they are, $|A \cap B| = 0$, simplifying calculations!