To solve the given problem:

Given:

• $A = \{a, b, c, d\}$
• $B = \{e, f, g, h\}$
• $U = \{a, b, c, d, e, f, g, h\}$

You need to find:

1. $A \cup B$ (the union of $A$ and $B$).
2. $A'$ (the complement of $A$ relative to the universal set $U$).

Solution:

i) $A \cup B$:

The union of $A$ and $B$ includes all the elements that are in $A$ or $B$ (or both). $A \cup B = \{a, b, c, d, e, f, g, h\}$

ii) $A'$:

The complement of $A$ ($A'$) consists of all elements in the universal set $U$ that are not in $A$. $A' = U - A = \{e, f, g, h\}$

Final Answer:

1. $A \cup B = \{a, b, c, d, e, f, g, h\}$
2. $A' = \{e, f, g, h\}$

Would you like more details or have any questions?

Expanding Questions:

1. What is the difference between union and intersection of sets?
2. How is the complement of a set defined in set theory?
3. What is the relationship between the universal set and its subsets?
4. Can you define $B'$ for the given universal set $U$?
5. How would the solution change if $A \cap B \neq \emptyset$?

Tip:

To solve set problems quickly, draw Venn diagrams to visualize relationships.