1. **Problem Statement:** (a) Shade the set $A' \cup B'$ where $A'$ and $B'$ are complements of sets $A$ and $B$ respectively. (b) Shade the set $(A \cup B)'$, the complement of the union of $A$ and $B$. (c) Determine if $A' \cup B'$ and $(A \cup B)'$ are equal. 2. **Relevant Formulas and Rules:** - The complement of a set $A$, denoted $A'$, contains all elements in the universal set $U$ that are not in $A$. - The union of two sets $A$ and $B$, denoted $A \cup B$, contains all elements in $A$, $B$, or both. - De Morgan's Laws state: $$ (A \cup B)' = A' \cap B' $$ $$ (A \cap B)' = A' \cup B' $$ 3. **Step-by-step Solution:** **(a) Shade $A' \cup B'$:** - $A'$ is everything outside $A$. - $B'$ is everything outside $B$. - Their union $A' \cup B'$ includes all elements not in $A$ or not in $B$. - This means all elements outside $A$ and all elements outside $B$ are shaded. **(b) Shade $(A \cup B)'$:** - $A \cup B$ is all elements in $A$ or $B$. - Its complement $(A \cup B)'$ is all elements not in $A$ or $B$. - So, shade the region outside both $A$ and $B$. **(c) Are $A' \cup B'$ and $(A \cup B)'$ equal?** - By De Morgan's Law, $(A \cup B)' = A' \cap B'$. - $A' \cup B'$ is the union, not the intersection. - Therefore, $A' \cup B' \neq (A \cup B)'$. 4. **Summary:** - The shaded region for (a) includes all elements outside $A$ or outside $B$ (more area shaded). - The shaded region for (b) includes only elements outside both $A$ and $B$ (less area shaded). - Hence, the answer to (c) is **No**, the sets are not equal. **Final answer:** - (a) Shade $A' \cup B'$ (outside $A$ or outside $B$). - (b) Shade $(A \cup B)'$ (outside both $A$ and $B$). - (c) $A' \cup B' \neq (A \cup B)'$; answer is **No**.