https://file.aiquickdraw.com/mathbot/file/1726018095979jjkqkjmw.jpg

Let's analyze the problem from the image you provided. Here's the information from the problem:

- The set \( C \) is defined as \( C = \{ z \mid z \geq 2 \} \), meaning it includes all real numbers greater than or equal to 2.
- The set \( D \) is defined as \( D = \{ z \mid z \leq 5 \} \), meaning it includes all real numbers less than or equal to 5.

### Union of \( C \) and \( D \) ( \( C \cup D \) )
The union of two sets \( C \cup D \) includes all elements that are in either set \( C \) or set \( D \), or in both. 

- \( C \) is all real numbers greater than or equal to 2, so it is the interval \( [2, \infty) \).
- \( D \) is all real numbers less than or equal to 5, so it is the interval \( (-\infty, 5] \).

Thus, the union of these two sets will cover all real numbers because there is overlap between \( C \) and \( D \). So, \( C \cup D = (-\infty, \infty) \), which includes all real numbers.

### Intersection of \( C \) and \( D \) ( \( C \cap D \) )
The intersection of two sets \( C \cap D \) includes only the elements that are in both sets \( C \) and \( D \).

- \( C \) is \( [2, \infty) \), so it only includes numbers starting from 2.
- \( D \) is \( (-\infty, 5] \), so it only includes numbers up to 5.

The overlap between these two sets is the interval from 2 to 5. Therefore, \( C \cap D = [2, 5] \).

### Final Answer:
- \( C \cup D = (-\infty, \infty) \)
- \( C \cap D = [2, 5] \)

Let me know if you'd like further details or clarifications!

Here are 5 related questions for practice:
1. What is the union of \( (-\infty, 0) \) and \( [3, \infty) \)?
2. How do you find the intersection of \( (-2, 4] \) and \( [0, \infty) \)?
3. What does the intersection of \( (-\infty, -3] \) and \( (0, 5) \) look like?
4. If \( A = [0, 3] \) and \( B = [2, 6] \), what is \( A \cap B \)?
5. What is the union of \( [0, 1] \) and \( [2, 3] \)?

Tip: When finding intersections, focus on the common overlapping range between the sets.

C and D are sets of real numbers defined as follows: C = {z | z ≥ 2}, D = {z | z ≤ 5}. Write C ∪ D and C ∩ D using interval notation. If the set is empty, write ∅.

Learn how to find the union and intersection of sets C = {z | z ≥ 2} and D = {z | z ≤ 5} using interval notation. The problem involves basic set theory and covers concepts such as interval notation, union, and intersection.

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