1. Problem: Show $A \cup B$ by Venn diagram for: (i) Disjoint sets: Two circles representing $A$ and $B$ that do not overlap. (ii) Overlapping sets: Two circles intersecting partially, shading entire $A$ and $B$ areas. (iii) $A$ subset of $B$: Small circle $A$ inside larger circle $B$, shade all of $B$. 2. Problem: Show $A \cap B$ by Venn diagram for: (i) $B$ subset of $A$: Small circle $B$ inside $A$, shade all of $B$. (ii) Overlapping sets: Two circles intersecting, shade their intersection region. (iii) Disjoint sets: Two separate circles, no intersection shaded (empty set). 3. Problem: Find $A-B$ and $B-A$ with Venn diagrams when: (i) Overlapping: Shade $A$ region outside intersection for $A-B$, shade $B$ region outside intersection for $B-A$. (ii) $A$ subset of $B$: $A-B$ is empty (no region outside $B$), $B-A$ is $B$ excluding $A$. 4. Problem: Find $A-B$ and $B-A$ with Venn diagrams when: (i) Disjoint sets: $A-B$ is entire $A$, $B-A$ is entire $B$. (ii) $B$ subset of $A$: $A-B$ is $A$ excluding $B$, $B-A$ is empty. 5-8. Let $U=\{1,2,3,4,5,6,7\}, A=\{1,2,4,6\}, B=\{2,3,5\}, C=\{1,3,6\}$. 5. Complements: $A^c=U\setminus A=\{3,5,7\}$, $B^c=\{1,4,6,7\}$, $C^c=\{2,4,5,7\}$. 6. Unions and intersections: $A \cup B = \{1,2,3,4,5,6\}$, $A \cap B = \{2\}$. 7. $A \cup C = \{1,2,3,4,6\}$, $B \cap C = \{3\}$. 8. $A^c \cap B^c = \{4,6,7\}$. 9. Verify $A-B = A \cap B^c$ for overlapping $A$ and $B$: Both represent elements in $A$ not in $B$. 10. Verify $(A-B)^c = A^c \cup B$ for disjoint $A,B$: complement of $A$ minus $B$ equals union of complements. 11. Verify DeMorgan's law: $(A \cup B)^c = A^c \cap B^c$ for overlapping sets. 12. Verify $(A \cap B)^c = A^c \cup B^c$ taking $A \subseteq B$. 13. Show $(A \cup B)^c = A^c \cap B^c$ where $A,B$ disjoint. 14. English alphabets: $A$ vowels, $B$ consonants, verify DeMorgan's laws with complements and intersections/unions. 15. Verify $(A \cup B) \cup C = A \cup (B \cup C)$ for $A, C$ disjoint, $A \subseteq B$, $B$ and $C$ overlapping. 16. Verify associativity: $(A \cap B) \cap C = A \cap (B \cap C)$ with specified overlaps and disjoint conditions. 17. Identify diagrams: a. $A$ inside $B$ represents $A$ subset of $B$ (e.g., cats inside dogs not logical, but mathematical subset). b. Non-overlapping $A,B$ for disjoint sets (e.g., apples and fruit? no, apples are fruit, so incorrect). c. Overlapping circles for overlapping sets (e.g., high school runners and swimmers can overlap). 18-23. Draw Venn diagrams and explain relationships: 18. Teachers and women: overlapping sets depending on gender composition. 19. Wrestlers and grey-haired people: possibly overlapping or disjoint. 20. Shirts and clothing: shirts subset of clothing. 21. Poets and plumbers: generally disjoint. 22. Cats and pets: cats subset of pets. 23. University students and employees: overlapping sets. 24. Venn diagram of number sets: natural numbers inside whole numbers; integers include whole numbers and negatives; rationals include integers; reals include rationals and irrationals; irrational numbers are real numbers not rational. 25. Blood Types: draw Venn diagram with sets A,B,O Rh+/- representing blood type presence. 26-30. Three-set Venn diagrams for professions or categories; show all intersections and unique parts with explanations. Final note: Venn diagrams are visual tools; descriptions above provide how to shade and interpret each case.