1. **Problem:** Show $A \cup B$ by Venn diagram in different cases. 1.1. When $A$ and $B$ are disjoint sets, $A \cup B$ is the entire area covered by circles $A$ and $B$ without any overlap. 1.2. When $A$ and $B$ overlap, $A \cup B$ includes all elements in $A$, in $B$, and in their intersection. 1.3. When $A$ is a subset of $B$, $A \cup B$ equals $B$ entirely. 2. **Problem:** Show $A \cap B$ by Venn diagram in different cases. 2.1. When $A$ and $B$ are disjoint, $A \cap B$ is empty (no overlap). 2.2. When $A$ and $B$ overlap, $A \cap B$ is the overlapping area. 2.3. When $A$ is subset of $B$, $A \cap B = A$. 3. **Problem:** Find $A-B$ and $B-A$ using Venn diagrams. 3.1. If $A$ and $B$ overlap, $A-B$ is the part of $A$ outside $B$, and $B-A$ is the part of $B$ outside $A$. 3.2. If they are disjoint, $A-B = A$ and $B-A = B$ since there is no overlap. 4. **Problem:** Find $A-B$ and $B-A$ when: 4.1. $A$ and $B$ are disjoint sets: same as 3.2. 4.2. $B$ is subset of $A$: $A-B$ is elements in $A$ not in $B$, and $B-A$ is empty. 5. & 6. & 7. & 8. Problems involve visualizing unions and intersections like $A$, $B^c$, $C$, $A \cup B$, $A \cap B$, $A \cup C$, $B \cap C$, $A \cap B^c$ using Venn diagrams. 9. Verify $A-B = A \cap B^c$ for overlapping sets: Elements in $A$ but not in $B$ is same as elements in $A$ intersecting complement of $B$. 10. Verify $(A-B)^c= A^c \cup B$ for disjoint sets by showing complements and unions. 11.-13. Verify DeMorgan's Laws: - $(A \cup B)^c = A^c \cap B^c$ - $(A \cap B)^c = A^c \cup B^c$ Shown using Venn diagrams with different relations. 14. English alphabets with vowels ($A$) and consonants ($B$) and verify DeMorgan's laws. 15.-16. Complex verification of DeMorgan's laws with additional conditions (disjoint, subsets, overlaps). 17. Identify correct Venn diagrams per description. 18.-23. Draw and explain Venn diagrams of pairs (teachers-women, wrestlers-grey-haired, etc) showing their relationships. 24. Draw nested Venn diagram for natural numbers, whole numbers, integers, rationals, and real numbers and identify irrational numbers outside rational set. 25. Draw Venn diagram representing blood type sets and percentages. 26.-30. Draw three-circle Venn diagrams (eight regions) for groups like poets-playwrights-painters, women-politicians-chefs, authors-editors-publishers, doctors-nurses-patients, teachers-swimmers-tall people, labeling each region with member explanation or empty set. **Summary:** These exercises reinforce understanding of unions, intersections, complements, differences, subsets, and DeMorgan’s laws through Venn diagrams.