The question asks which expression represents the intersection of sets $A$ and $B$. The intersection of two sets $A$ and $B$ is denoted by $A \cap B$.

Analysis of the Options:

1. $A' \cup B'$: This represents the union of the complements of $A$ and $B$, which is the complement of $A \cap B$ by De Morgan's laws, not the intersection.
2. $P(A \cap B)$: This represents the probability of the intersection of $A$ and $B$, not the intersection itself.
3. $A \cup B$: This represents the union of sets $A$ and $B$, which is the set of elements in either $A$ or $B$, not just those in both.
4. $A \cap B$: This correctly represents the intersection of sets $A$ and $B$, which is the set of elements that are in both $A$ and $B$.

Conclusion:

The correct answer is the last option, $A \cap B$.

Would you like more details on set theory or have any other questions?

Here are some related questions:

1. What is the union of two sets and how is it represented?
2. What do De Morgan's laws state in set theory?
3. How is the complement of a set defined?
4. Can you explain the difference between intersection and union of sets?
5. How do you calculate the probability of the intersection of two events?

Tip: When working with set operations, remember that $\cap$ is used for intersection (common elements), and $\cup$ is used for union (all elements in either set).