The image contains an exercise from a mathematics textbook focused on set theory. It defines the following sets:

• $T = \{m, n, o, p, q, r\}$
• $A = \{m, n, o\}$
• $B = \{p, q, o, r\}$
• $C = \{o, n, r\}$

The task asks to perform several operations involving union, intersection, and differences among these sets. The specific operations listed are:

1. $A \cap B$
2. $A \cup C$
3. $A \cup B$
4. $A \cup (B \cap C)$
5. $(A \cup B) \cap C$
6. $(A \cap C) \cup B$
7. $(A \cup C) \cap (B \cup C)$
8. $(A \cap C) \cap B$
9. $(A \cup B) \cap (A \cup C)$
10. $A \setminus B$
11. $A \setminus C$
12. $(A \setminus B) \cap C$
13. $A \setminus (B \cap C)$
14. $(A \cup C) \setminus B$
15. $(A \setminus C) \cap B$
16. $(A \cup C) \setminus (B \cup C)$
17. $(A \cap B) \setminus C$
18. $A \cup (B \setminus C)$
19. $(A \setminus C) \setminus B$
20. $(A \cap C) \setminus (B \cap C)$

Let's go through solving a few of these operations.

1. $A \cap B$ (Intersection of A and B): This operation finds the elements common to both sets $A$ and $B$. $A \cap B = \{o\}$

2. $A \cup C$ (Union of A and C): This operation combines all elements from sets $A$ and $C$, removing duplicates. $A \cup C = \{m, n, o, r\}$

3. $A \cup B$ (Union of A and B): This operation combines all elements from sets $A$ and $B$, removing duplicates. $A \cup B = \{m, n, o, p, q, r\}$

Would you like to go through the rest of the operations in detail or have any specific ones you'd like to focus on?

Additional Questions

1. How do you compute the intersection of two sets in general?
2. What is the difference between union and intersection operations in set theory?
3. How can you represent the set difference $A \setminus B$ using a Venn diagram?
4. What are the properties of the union and intersection operations (commutativity, associativity)?
5. How do you approach solving problems with more complex operations, such as combining union, intersection, and difference?

Tip:

When solving set theory problems, using Venn diagrams can help visualize relationships between sets, making it easier to understand and solve complex set operations.