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Let's go through the problem step-by-step.

The sets given are:
\[
A = \langle -2, 3 \rangle \cup (5, \infty)
\]
\[
B = \langle -1, 7 \rangle
\]

### Part (1): Set Operations on \( A \) and \( B \)
Let's calculate each operation for the sets \( A \) and \( B \):

1. **Union** \( A \cup B \):
   The union of \( A \) and \( B \) includes all elements in either \( A \) or \( B \).

2. **Intersection** \( A \cap B \):
   The intersection includes only elements that are in both \( A \) and \( B \).

3. **Difference** \( A \setminus B \):
   The difference \( A \setminus B \) includes elements that are in \( A \) but not in \( B \).

4. **Difference** \( B \setminus A \):
   The difference \( B \setminus A \) includes elements that are in \( B \) but not in \( A \).

5. **Complement of A** \( A' \):
   The complement of \( A \) includes elements not in \( A \), assuming the universal set is all real numbers.

6. **Complement of B** \( B' \):
   The complement of \( B \) includes elements not in \( B \), assuming the universal set is all real numbers.

### Part (2): Cartesian Product \( A \times B \) and \( B \times A \)
This part requires calculating the Cartesian products of \( A \) and \( B \) as ordered pairs. These ordered pairs can then be plotted on a rectangular coordinate system.

I'll perform the calculations for each of these operations and display them.I've displayed the results of the set operations \( A \cup B \), \( A \cap B \), \( A \setminus B \), and \( B \setminus A \) for your review. Let me know if you would like further details on these results or any specific calculations.

Here are some related questions that might interest you:
1. How can we visualize these set operations on a number line?
2. What are the steps to calculate the complement of a set in the real number line?
3. How would the results change if \( A \) or \( B \) had closed or open intervals differently?
4. What is the Cartesian product of sets \( A \times B \) and \( B \times A \), and how would it be plotted?
5. How do these operations change when applying them to finite sets rather than intervals?

**Tip:** When dealing with intervals, always pay attention to whether they are open or closed, as this affects the inclusion of boundary points in the operations.

Zad. 7 (DOM) Wykonaj następujące działania: (1) A ∪ B, A ∩ B, A \ B, B \ A, A', B' na zbiorach A i B – zapisz wyniki oraz zaznacz na osi liczbowej (2) A × B, B × A na zbiorach A i B – zapisz wyniki zgodnie z definicją oraz zaznacz układzie prostokątnym dla zbiorów: A = ⟨-2, 3⟩ ∪ (5, ∞), B = ⟨-1, 7⟩

Solve set operations including union, intersection, set difference, and Cartesian product for the sets A = ⟨-2, 3⟩ ∪ (5, ∞) and B = ⟨-1, 7⟩. Learn how to represent these on a number line and in a coordinate system. Suitable for high school math students.

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