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Let's break down the given problem.

We have two sets \( F \) and \( E \) defined as:

- \( F = \{-1, 0, 1, 7\} \)
- \( E = \{-2, -1, 0, 4\} \)

### 1. **Union of \( F \) and \( E \)**

The union of two sets contains all the elements from both sets, without repeating any duplicates. So, we combine all elements from \( F \) and \( E \):

\[
F \cup E = \{-1, 0, 1, 7, -2, 4\}
\]

(Arranged typically in increasing order, but the order doesn't matter in sets.)

### 2. **Intersection of \( F \) and \( E \)**

The intersection of two sets contains only the elements that are present in both sets. From sets \( F \) and \( E \), the common elements are:

\[
F \cap E = \{-1, 0\}
\]

### Final Answers:
- **Union**: \( F \cup E = \{-2, -1, 0, 1, 4, 7\} \)
- **Intersection**: \( F \cap E = \{-1, 0\} \)

Let me know if you want any further details or if you have questions.

Here are 5 follow-up questions to help you explore related ideas:
1. How would the union and intersection change if an element was added to one of the sets?
2. Can you find the difference between sets \( F \) and \( E \)?
3. How do the union and intersection operations relate to Venn diagrams?
4. What would happen if one of the sets was empty?
5. Can you explain how the union and intersection are related to the concept of subsets?

**Tip**: Remember, in set notation, order doesn't matter, but elements are listed only once!

Find the union and intersection of the sets F = {-1, 0, 1, 7} and E = {-2, -1, 0, 4}. Write your answers using set notation (in roster form).

Learn how to find the union and intersection of the sets F = {-1, 0, 1, 7} and E = {-2, -1, 0, 4}. This problem explores key concepts in set theory, including the union and intersection of sets, perfect for students in Grades 7-9.

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