To find the universal set [tex]\( U \)[/tex], let's go through the steps step-by-step.
1. Identify the given sets:
[tex]\[
A = \{2, 3, 5, 7\}
\][/tex]
[tex]\[
A' = \{1, 4, 8\}
\][/tex]
2. Understanding the universal set [tex]\( U \)[/tex]:
The universal set [tex]\( U \)[/tex] contains all the elements that belong to either set [tex]\( A \)[/tex] or its complement [tex]\( A' \)[/tex]. This means that [tex]\( U \)[/tex] is the union of sets [tex]\( A \)[/tex] and [tex]\( A' \)[/tex].
3. Combine the elements of [tex]\( A \)[/tex] and [tex]\( A' \)[/tex]:
[tex]\[
U = A \cup A'
\][/tex]
4. Union of the sets:
[tex]\[
U = \{2, 3, 5, 7\} \cup \{1, 4, 8\}
\][/tex]
5. List all the unique elements in the union:
By combining the elements from both sets and ensuring no duplicates:
[tex]\[
U = \{1, 2, 3, 4, 5, 7, 8\}
\][/tex]
Thus, the universal set [tex]\( U \)[/tex] is:
[tex]\[
U = \{1, 2, 3, 4, 5, 7, 8\}
\][/tex]
