The Venn diagram in your image consists of two sets, $B$ and $D$, with the universal set $U$. You are asked to shade the region representing $B \cap D$, which is the intersection of sets $B$ and $D$.

In a Venn diagram, the intersection $B \cap D$ refers to the region where both sets overlap, which is the middle portion where the two circles overlap. This is the area common to both $B$ and $D$.

Solution:

To complete this task, you should shade the overlapping region of the two circles representing sets $B$ and $D$. This shaded region will represent all the elements that belong to both sets.

Do you have any questions or would you like further clarification?

Here are 5 related questions to expand on this:

1. What would the diagram look like if we wanted to shade $B \cup D$ (union of $B$ and $D$)?
2. What does the region outside both sets represent in terms of the universal set $U$?
3. How would the diagram change if we wanted to shade $B - D$ (difference of $B$ and $D$)?
4. Can a Venn diagram be used to represent more than two sets, and how does it look in that case?
5. How can Venn diagrams be useful in probability theory?

Tip: The intersection of sets always involves only the elements that are common to all sets being compared. In diagrams, this is always the overlapping region.