We are given three sets $M$, $N$, and $\mu$. $M$ contains integers $x$ such that $2 \le x \le 6$, $N$ contains integers $x$ such that $4 \le x \le 8$, and $\mu$ contains integers $x$ such that $1 \le x \le 10$. We need to find the intersection of the complement of $M$ ($M'$) and the complement of $N$ ($N'$).

1. Problem Description

We are given three sets $M$, $N$, and $\mu$. $M$ contains integers $x$ such that $2 \le x \le 6$, $N$ contains integers $x$ such that $4 \le x \le 8$, and $\mu$ contains integers $x$ such that $1 \le x \le 10$. We need to find the intersection of the complement of $M$ ($M'$) and the complement of $N$ ($N'$).

2. Solution Steps

First, let's determine the elements of each set.

$M = \{2, 3, 4, 5, 6\}$

$N = \{4, 5, 6, 7, 8\}$

$\mu = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$

Next, we find the complements of $M$ and $N$ with respect to $\mu$.

$M' = \mu - M = \{1, 7, 8, 9, 10\}$

$N' = \mu - N = \{1, 2, 3, 9, 10\}$

Finally, we find the intersection of $M'$ and $N'$.

$M' \cap N' = \{1, 7, 8, 9, 10\} \cap \{1, 2, 3, 9, 10\} = \{1, 9, 10\}$

3. Final Answer

The answer is C. $\{1, 9, 10\}$