Let's go through the Venn diagram shown in the image and solve the given questions one by one.

Given:

• The universal set $U$ is divided into two subsets $A$ and $B$, with their corresponding elements marked in the diagram.
• Elements labeled as $a, b, c, d, e, f, g$.

From the Venn diagram:

• $A$ is the set containing the elements $a, c, d$.
• $B$ is the set containing the elements $b, c, e$.
• The universal set $U$ contains $a, b, c, d, e, f, g$.

Let's answer each question:

1. $U$:
   The universal set contains all the elements present in the diagram.
   $U = \{a, b, c, d, e, f, g\}$

2. $A' \cup B'$ (Complement of A union complement of B):
   We need to find the elements that are not in $A$ or not in $B$.
   $A' = \{b, e, f, g\}$ (elements not in $A$)
   $B' = \{a, d, f, g\}$ (elements not in $B$)
   $A' \cup B' = \{a, b, d, e, f, g\}$

3. $A' \cap B'$ (Complement of A intersect complement of B):
   Elements that are not in $A$ and not in $B$.
   $A' \cap B' = \{f, g\}$

4. $A' \cap B$ (Complement of A intersect B):
   Elements that are not in $A$ but are in $B$.
   $A' \cap B = \{b, e\}$

5. $A \cup B'$ (A union complement of B):
   Elements that are in $A$ or not in $B$.
   $A \cup B' = \{a, c, d, f, g\}$

Let me know if you'd like any more details or explanations!

Relative Questions:

1. What is the difference between the union and intersection of two sets?
2. How do we find the complement of a set in a universal set?
3. Can you explain the logic behind finding $A' \cup B'$?
4. How would the sets change if a new element was added only to $A$?
5. Can you show an example where $A \cap B'$ has more elements?

Tip:

Always double-check set complements to ensure you've included all elements outside the specific set(s).