1. The problem asks to illustrate DeMorgan's Law: $$(A \cup B)^C = A^C \cap B^C$$ using Venn diagrams. 2. DeMorgan's Law states that the complement of the union of two sets is equal to the intersection of their complements. 3. Step-by-step explanation: 1. Consider two sets $A$ and $B$ represented by two overlapping circles. 2. The union $A \cup B$ includes all elements in $A$, or $B$, or both. 3. The complement $(A \cup B)^C$ includes all elements not in $A$ or $B$. 4. The complements $A^C$ and $B^C$ include all elements not in $A$ and not in $B$, respectively. 5. The intersection $A^C \cap B^C$ includes all elements not in $A$ and not in $B$ simultaneously. 4. Therefore, the shaded region representing $(A \cup B)^C$ is exactly the same as the shaded region representing $A^C \cap B^C$. 5. This confirms DeMorgan's Law visually: the area outside both circles (neither in $A$ nor $B$) is the same for both expressions. Final answer: DeMorgan's Law $$(A \cup B)^C = A^C \cap B^C$$ is illustrated by shading the area outside both $A$ and $B$ in the Venn diagram, showing both sides represent the same set.