The problem asks to shade $B \cup (C \cap A')'$ on the Venn diagram. Let's break this expression down step by step:

1. $A'$: This represents the complement of set $A$, meaning all the elements outside of set $A$ (in the universal set $U$).

2. $C \cap A'$: This is the intersection of set $C$ and $A'$, which refers to the elements that are in set $C$ but not in set $A$.

3. $(C \cap A')'$: This is the complement of $C \cap A'$, meaning it includes everything in the universal set $U$ except the elements in $C \cap A'$.

4. $B \cup (C \cap A')'$: Finally, this is the union of set $B$ and the complement of $C \cap A'$. So, you need to shade all the areas that belong to set $B$ as well as the areas outside of $C \cap A'$.

Now, referring to the Venn diagram:

• First, identify $C \cap A'$, which is the part of set $C$ that does not overlap with set $A$.
• Then, take the complement of that region, which would be everything except that part of set $C$ and outside of set $A$.
• Finally, shade all of set $B$ in the diagram and also include the regions that are part of the complement of $C \cap A'$.

This approach will give you the correct shaded area for $B \cup (C \cap A')'$.

Do you want more details or have any questions?

Here are 5 related questions:

1. What is the union of two sets in a Venn diagram?
2. How do you represent a complement of a set in Venn diagrams?
3. How does an intersection of two sets appear in a Venn diagram?
4. How do we shade multiple sets on a Venn diagram that include both union and intersection?
5. What happens when we take the complement of an intersection?

Tip: To master Venn diagrams, always break down complex expressions step by step to visualize each part clearly.