1. **Problem Statement:** We have two sets $A$ and $B$ with some common intersection. We need to indicate the following set relationships on a Venn diagram: i. $A'$ (complement of $A$) ii. $A' \cap B'$ (intersection of complements of $A$ and $B$) iii. $A' \cap B$ (intersection of complement of $A$ and $B$) iv. $A \cap B'$ (intersection of $A$ and complement of $B$) v. $A \cup B'$ (union of $A$ and complement of $B$) 2. **Key Concepts:** - The complement $A'$ consists of all elements not in $A$. - Intersection $\cap$ means elements common to both sets. - Union $\cup$ means elements in either set or both. 3. **Step-by-step Indications on Venn Diagram:** i. $A'$: Shade the entire area outside circle $A$. ii. $A' \cap B'$: Shade the area outside both $A$ and $B$ (the region outside both circles). iii. $A' \cap B$: Shade the part inside $B$ but outside $A$ (the part of $B$ circle excluding overlap with $A$). iv. $A \cap B'$: Shade the part inside $A$ but outside $B$ (the part of $A$ circle excluding overlap with $B$). v. $A \cup B'$: Shade all elements in $A$ plus all elements outside $B$ (this includes all of $A$ and everything outside $B$ circle). 4. **Explanation:** - For complements, think "everything not in the set". - Intersections require overlapping shaded regions. - Unions combine shaded regions of both sets. 5. **Summary:** Each expression corresponds to a specific region in the Venn diagram of two sets $A$ and $B$.