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In the given problem, we are provided with two sets of real numbers:

- \( E = \{ w \mid w < 3 \} \), which means all real numbers less than 3.
- \( F = \{ w \mid w \geq 6 \} \), which means all real numbers greater than or equal to 6.

### 1. **Union of \(E\) and \(F\) (\( E \cup F \)):**
The union combines all elements from both sets. In this case, \( E \cup F \) represents all numbers less than 3 or greater than or equal to 6. Therefore, in interval notation:
\[
E \cup F = (-\infty, 3) \cup [6, \infty)
\]

### 2. **Intersection of \(E\) and \(F\) (\( E \cap F \)):**
The intersection includes only those elements common to both sets. However, since there are no numbers that are both less than 3 and greater than or equal to 6, the intersection is empty:
\[
E \cap F = \emptyset
\]

### Final answers:
- \( E \cup F = (-\infty, 3) \cup [6, \infty) \)
- \( E \cap F = \emptyset \)

Would you like more details on interval notation or union and intersection of sets? 

Here are 5 related questions you might find interesting:
1. How do you represent the complement of a set in interval notation?
2. Can the union of two sets ever be smaller than either of the sets?
3. What happens if the intervals overlap in a union or intersection problem?
4. How do you represent the union of finite sets in interval notation?
5. What is the difference between open and closed intervals in set theory?

**Tip:** When working with unions and intersections, sketching a number line can help visualize the intervals!

E and F are sets of real numbers defined as follows: E = {w | w < 3} and F = {w | w ≥ 6}. Write E ∪ F and E ∩ F using interval notation. If the set is empty, write ∅.

Understand how to find the union and intersection of sets E = {w | w < 3} and F = {w | w ≥ 6} using interval notation. This example demonstrates the application of set theory concepts and interval notation, suitable for Grades 9-11.

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