The image you provided shows two exercises related to set theory, specifically operations on sets. Here are the details of the exercises:

Exercise 2.2.23:

This exercise asks you to consider the following:

Let $A$ be the set of $n \times n$ real symmetric matrices, and $B$ the set of $n \times n$ real skew-symmetric matrices. The task is to describe the elements of $A \setminus B$ (the set difference between $A$ and $B$).

Exercise 2.2.24:

For any two sets $A$ and $B$, prove the following identity: $(A \cup B) \setminus (A \cap B) = (A \setminus B) \cup (B \setminus A)$ This is known as the symmetric difference between sets $A$ and $B$, which shows that the elements in $A \cup B$, but not in $A \cap B$, are exactly those that are in either $A$ or $B$ but not in both.

Would you like a detailed explanation or solution to any of these exercises?

Here are some questions to expand your understanding:

1. What is the geometric interpretation of the symmetric and skew-symmetric matrix sets?
2. What are the key properties of a symmetric matrix that are used in set operations?
3. How does the concept of set difference apply to matrix sets in Exercise 2.2.23?
4. What is the difference between set union and intersection in terms of matrix properties?
5. Can you think of a visual example to represent the symmetric difference identity in Exercise 2.2.24?

Tip: When working with set operations, always start by considering Venn diagrams—they provide a clear visual interpretation that simplifies many proofs or verifications.