To define set $A$ in terms of $B$ and $B'$ (the complement of $B$), we observe the following from the Venn diagram:

• Set $A$ is the circle on the left.
• Part of $A$ overlaps with $B$, and part of $A$ is outside of $B$, but still within the universal set $U$.

Therefore, the set $A$ can be expressed as: $A = (A \cap B') \cup (A \cap B)$

This states that set $A$ includes both the parts of $A$ that do not intersect with $B$ (i.e., $A \cap B'$) and the parts that do intersect with $B$ (i.e., $A \cap B$).

Let me know if you'd like more details or have any questions.

Here are five related questions to explore further:

1. How would you define set $B$ in terms of $A$ and $A'$?
2. What is the complement of set $A$ in terms of $B$ and $B'$?
3. How can the universal set $U$ be expressed using sets $A$, $B$, and their complements?
4. How can the intersection $A \cap B$ be expressed using set operations?
5. What is the relationship between $A \cup B$ and the universal set $U$?

Tip: In Venn diagrams, intersections and unions help visually represent how different sets overlap and relate to each other within a universal set.