Let's analyze each set step by step:

1. Complement of A (denoted as $\overline{A}$): The complement of A includes all the elements of the Universal set $U$ that are not in set $A$.

   Universal set $U = \{a, b, c, d, e, 1, 2, 3\}$
   Set $A = \{2, 1, 3, a, b\}$

   So, $\overline{A} = U - A = \{c, d, e\}$

   Therefore,
   $\overline{A} = \{c, d, e\}$

2. Union of $A$ and complement of $B$ (denoted as $A \cup \overline{B}$): The complement of $B$ includes all the elements of $U$ that are not in set $B$.

   Set $B = \{c, 1, d\}$

   So,
   $\overline{B} = U - B = \{a, b, e, 2, 3\}$

   Now, the union of $A$ and $\overline{B}$ is the set of all elements that are in either $A$ or $\overline{B}$, or in both:

   $A \cup \overline{B} = \{2, 1, 3, a, b\} \cup \{a, b, e, 2, 3\} = \{1, 2, 3, a, b, e\}$

   Therefore,
   $A \cup \overline{B} = \{1, 2, 3, a, b, e\}$

3. Intersection of $\overline{A}$ and $\overline{B}$ (denoted as $\overline{A} \cap \overline{B}$): The intersection includes elements that are in both $\overline{A}$ and $\overline{B}$.

   From step 1,
   $\overline{A} = \{c, d, e\}$
   From step 2,
   $\overline{B} = \{a, b, e, 2, 3\}$

   The common element in both sets is $e$.

   Therefore,
   $\overline{A} \cap \overline{B} = \{e\}$

Final Results:

1. $\overline{A} = \{c, d, e\}$
2. $A \cup \overline{B} = \{1, 2, 3, a, b, e\}$
3. $\overline{A} \cap \overline{B} = \{e\}$

Would you like further details or explanations on any of these? Here are 5 questions related to this topic to help you expand your understanding:

1. What is the complement of a set, and how is it calculated?
2. How do we find the union of two sets?
3. What is the intersection of two sets and how is it determined?
4. Can a complement and union operation ever result in the same set?
5. How does the universal set affect the complement of subsets within it?

Tip: Always start by finding the complement of sets when dealing with complement operations. This simplifies the process of solving complex set problems.