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The problem asks to write the union \( E \cup F \) and the intersection \( E \cap F \) using interval notation, where the sets \( E \) and \( F \) are defined as follows:

\[
E = \{ x \mid x < 1 \}
\]
\[
F = \{ x \mid x \geq 6 \}
\]

### Step 1: Union (\( E \cup F \))
The union of two sets includes all elements that are in either set.

- For \( E \), all real numbers less than 1 are included, i.e., \( (-\infty, 1) \).
- For \( F \), all real numbers greater than or equal to 6 are included, i.e., \( [6, \infty) \).

Thus, the union of \( E \) and \( F \) is:
\[
E \cup F = (-\infty, 1) \cup [6, \infty)
\]

### Step 2: Intersection (\( E \cap F \))
The intersection of two sets includes only the elements that are in both sets.

- For \( E \), the elements are less than 1.
- For \( F \), the elements are greater than or equal to 6.

Since there is no overlap between these two sets, their intersection is empty:
\[
E \cap F = \emptyset
\]

So, the answers are:

- \( E \cup F = (-\infty, 1) \cup [6, \infty) \)
- \( E \cap F = \emptyset \)

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

Here are 5 related questions you can explore:

1. What is the union of \( (-\infty, 0) \) and \( [2, \infty) \)?
2. How do you find the intersection of two overlapping intervals, like \( (-\infty, 3) \) and \( [1, 5) \)?
3. Can two disjoint sets ever have a non-empty intersection?
4. How do you represent an empty set in set notation?
5. How do interval notations differ for open and closed sets?

**Tip:** When working with unions and intersections, always visualize the number line to clearly see where the intervals overlap or combine.

Write the union (E ∪ F) and intersection (E ∩ F) using interval notation for the sets defined as E = {x | x < 1} and F = {x | x ≥ 6}.

Learn how to find the union and intersection of two sets defined in interval notation. This example covers the sets E = {x | x < 1} and F = {x | x ≥ 6} and demonstrates how to express their union and intersection. Suitable for high school mathematics students.

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