Complement Intersection 25A281
1. **State the problem:** We need to shade the complement of the intersection of sets $C$ and $A$, denoted as $(C \cap A)'$.
2. **Recall definitions:**
- The intersection $C \cap A$ is the set of elements common to both $C$ and $A$.
- The complement $(C \cap A)'$ is everything in the universal set $U$ that is *not* in $C \cap A$.
3. **Express the complement using set operations:**
$$(C \cap A)' = U - (C \cap A)$$
4. **Use De Morgan's Law:**
De Morgan's Law states:
$$ (C \cap A)' = C' \cup A' $$
This means the complement of the intersection is the union of the complements.
5. **Interpretation for shading:**
- Shade all areas outside $C$ (i.e., $C'$) and all areas outside $A$ (i.e., $A'$).
- This includes everything except the overlapping region of $C$ and $A$.
6. **Summary:**
To shade $(C \cap A)'$, shade all parts of the universal set except the region where $C$ and $A$ overlap.
**Final answer:**
$$(C \cap A)' = C' \cup A'$$
This means shade all areas outside the intersection of $C$ and $A$.