Let's analyze the problem step by step.

We have two sets defined as:

• $C = \{ x \mid x > 2 \}$, which means all numbers greater than 2.
• $D = \{ x \mid x \geq 6 \}$, which means all numbers greater than or equal to 6.

Now, let's determine the union and intersection in interval notation.

Union: $C \cup D$

The union consists of all elements that belong to either set $C$ or set $D$. Since $C$ includes all numbers greater than 2, and $D$ includes all numbers starting from 6, the union remains:

$C \cup D = \{ x \mid x > 2 \}$

Interval notation: $(2, \infty)$

Intersection: $C \cap D$

The intersection consists of all elements that belong to both $C$ and $D$. Since $C$ includes numbers greater than 2, and $D$ includes numbers starting from 6, the overlap is:

$C \cap D = \{ x \mid x \geq 6 \}$

Interval notation: $[6, \infty)$

Final Answers

• $C \cup D = (2, \infty)$
• $C \cap D = [6, \infty)$

Now, you can input these intervals into the system. Let me know if you have any questions!

Here are 5 related questions for further exploration:

1. How do unions and intersections change when dealing with closed intervals?
2. What is the difference between strict inequalities ($>, <$) and non-strict inequalities ($\geq, \leq$) in interval notation?
3. How would the result change if $D = \{ x \mid x > 6 \}$ instead?
4. Can two disjoint sets ever have a non-empty union?
5. How does interval notation relate to set-builder notation?

Tip: Always visualize number lines when working with unions and intersections to better understand the relationships between sets!