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The image contains the following problem:

Let \( f \) and \( g \) be sets of real numbers defined as follows:

\[
f = \{x \mid x \leq 6\}
\]

\[
g = \{x \mid x \geq 8\}
\]

We need to find:

1. \( f \cap g \) (the intersection of \( f \) and \( g \))
2. \( f \cup g \) (the union of \( f \) and \( g \))

If the set is empty, we should write \( \emptyset \).

### Solutions:

1. **Intersection (\( f \cap g \)):**
   - \( f \cap g \) represents the common elements between sets \( f \) and \( g \).
   - From the definitions, \( f = \{x \mid x \leq 6\} \) and \( g = \{x \mid x \geq 8\} \).
   - There are no elements that satisfy both conditions \( x \leq 6 \) and \( x \geq 8 \) simultaneously.
   - Therefore, \( f \cap g = \emptyset \).

2. **Union (\( f \cup g \)):**
   - \( f \cup g \) represents all elements that are in either set \( f \) or set \( g \).
   - For \( f = \{x \mid x \leq 6\} \) and \( g = \{x \mid x \geq 8\} \), the union combines all values less than or equal to 6 with all values greater than or equal to 8.
   - Therefore, \( f \cup g = \{x \mid x \leq 6 \text{ or } x \geq 8\} \).

### Final Answers:

1. \( f \cap g = \emptyset \)
2. \( f \cup g = \{x \mid x \leq 6 \text{ or } x \geq 8\} \)

Would you like any further details or have any questions?

Here are some related questions:

1. How do we find the intersection and union of more complex sets?
2. What are some real-life applications of set intersections and unions?
3. How would the result change if \( f \) and \( g \) had overlapping values?
4. Can we represent these sets and their operations visually using a number line or Venn diagrams?
5. What are the properties of sets and operations like intersection and union?

**Tip:** When working with set operations, always consider visualizing the problem using Venn diagrams or a number line for better understanding!

Let f and g be sets of real numbers defined as follows: f = {x | x <= 6}, g = {x | x >= 8}. Find f ∩ g and f ∪ g. If the set is empty, write Ø.

Learn how to find the intersection and union of two sets: f = {x | x ≤ 6} and g = {x | x ≥ 8}. This problem demonstrates the concepts of set operations, focusing on the properties of intersection and union, suitable for students in Grades 9-12.

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