The task involves set operations based on the universal set $U = \{a, b, c, d, e, f\}$ and two subsets $A = \{a, c, e\}$ and $B = \{d, e, f\}$. I will compute each requested set operation step by step. Here are the results:

1. $A \cup B$ (Union of $A$ and $B$):

$A \cup B = \{a, c, e\} \cup \{d, e, f\} = \{a, c, e, d, f\}.$

2. $A \cap B$ (Intersection of $A$ and $B$):

$A \cap B = \{a, c, e\} \cap \{d, e, f\} = \{e\}.$

3. $B - A$ (Elements in $B$ but not in $A$):

$B - A = \{d, e, f\} - \{a, c, e\} = \{d, f\}.$

4. $A - B$ (Elements in $A$ but not in $B$):

$A - B = \{a, c, e\} - \{d, e, f\} = \{a, c\}.$

5. Complement of $A$, $A^c$:

$A^c = U - A = \{a, b, c, d, e, f\} - \{a, c, e\} = \{b, d, f\}.$

6. Complement of $B$, $B^c$:

$B^c = U - B = \{a, b, c, d, e, f\} - \{d, e, f\} = \{a, b, c\}.$

7. $A^c \cup B$ (Union of the complement of $A$ and $B$):

$A^c \cup B = \{b, d, f\} \cup \{d, e, f\} = \{b, d, e, f\}.$

8. $A^c \cap B$ (Intersection of the complement of $A$ and $B$):

$A^c \cap B = \{b, d, f\} \cap \{d, e, f\} = \{d, f\}.$

9. $A^c \cap B^c$ (Intersection of the complements of $A$ and $B$):

$A^c \cap B^c = \{b, d, f\} \cap \{a, b, c\} = \{b\}.$

10. $A^c \cup B^c$ (Union of the complements of $A$ and $B$):

$A^c \cup B^c = \{b, d, f\} \cup \{a, b, c\} = \{a, b, c, d, f\}.$

Let me know if you would like any step clarified further or have any additional questions.

Here are 5 related questions to expand your understanding:

1. How do we represent the complement of a set in a Venn diagram?
2. What is the symmetric difference of sets $A$ and $B$?
3. Can the intersection of a set and its complement ever be non-empty?
4. How does the universal set influence the calculation of complements?
5. How do we verify the results of set operations using diagrams?

Tip: Always list elements in a set operation result systematically to avoid missing or duplicating any elements.