Given sets A = 1, 2, 3, 4, B = 2, 4, 6, 8, and C = 3, 4, 5, 6, find the set differences A - B, B - C, and B - B.

The set difference $A - B$ contains all elements that are in set A but not in set B.

$$A - B = \{x \mid x \in A \text{ and } x \notin B\}$$ $$A - B = \{1, 2, 3, 4\} - \{2, 4, 6, 8\}$$

The elements common to A and B are $\{2, 4\}$. Removing these from A gives:

$$A - B = \{1, 3\}$$

The set $A - B$ is $\boxed{\{1, 3\}}$.

The set difference $B - C$ contains all elements that are in set B but not in set C.

$$B - C = \{x \mid x \in B \text{ and } x \notin C\}$$ $$B - C = \{2, 4, 6, 8\} - \{3, 4, 5, 6\}$$

The elements common to B and C are $\{4, 6\}$. Removing these from B gives:

$$B - C = \{2, 8\}$$

The set $B - C$ is $\boxed{\{2, 8\}}$.

The set difference $B - B$ contains all elements that are in set B but not in set B.

$$B - B = \{x \mid x \in B \text{ and } x \notin B\}$$

This means there are no elements that satisfy both conditions, resulting in an empty set.

$$B - B = \{2, 4, 6, 8\} - \{2, 4, 6, 8\}$$ $$B - B = \emptyset$$

The set $B - B$ is $\boxed{\emptyset}$.