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.