https://file.aiquickdraw.com/mathbot/file/1726021094133qpf6k421.jpg

From the image, it appears that you need to find the union and intersection of the sets \( D \) and \( E \) defined as follows:

- \( D = \{v \mid v > 1\} \)
- \( E = \{v \mid v \geq 25\} \)

### Union \( D \cup E \)
The union of two sets contains all the elements that are in either set. Since set \( E \) starts at 25 and includes all greater numbers, and set \( D \) starts at just above 1, the union of \( D \) and \( E \) is all values greater than 1. Thus, in interval notation, this is:
\[ D \cup E = (1, \infty) \]

### Intersection \( D \cap E \)
The intersection of two sets contains only the elements that are in both sets. The elements common to both \( D \) and \( E \) are those starting from 25 and onwards because \( E \) begins at 25 and \( D \) includes all numbers greater than 1. Therefore, the intersection in interval notation is:
\[ D \cap E = [25, \infty) \]

Would you like any further explanations on these solutions or have another question on this topic? Here are some related questions you might consider:

1. How would you represent the set difference \( D \setminus E \) in interval notation?
2. What is the complement of \( D \cup E \) relative to the real numbers?
3. How would the union change if \( E = \{v \mid v > 25\} \) instead?
4. How do open and closed intervals work in set notation?
5. What is the significance of including or excluding the endpoint in an interval?

Tip: Remember, in interval notation, round brackets mean the endpoint is not included, while square brackets mean it is included.

D and E are sets of real numbers defined as follows: D = {v | v > 1} and E = {v | v >= 25}. Write D ∪ E and D ∩ E using interval notation.

Explore how to find the union and intersection of sets D = {v | v > 1} and E = {v | v >= 25} using interval notation. This problem highlights key concepts in set theory and inequalities, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation