To solve this problem, we need to find the complements of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] relative to the universal set [tex]\( U \)[/tex].
### Finding the Complement of Set [tex]\( A \)[/tex]:
1. List the elements in the universal set [tex]\( U \)[/tex]:
[tex]\[
U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
\][/tex]
2. List the elements in set [tex]\( A \)[/tex]:
[tex]\[
A = \{1, 4, 7, 10\}
\][/tex]
3. Identify the elements in [tex]\( U \)[/tex] that are not in [tex]\( A \)[/tex]:
- The elements of [tex]\( U \)[/tex] that are not in [tex]\( A \)[/tex] are:
[tex]\[
\{2, 3, 5, 6, 8, 9\}
\][/tex]
4. The complement of set [tex]\( A \)[/tex] ([tex]\( A' \)[/tex]) consists of these elements:
[tex]\[
A' = \{2, 3, 5, 6, 8, 9\}
\][/tex]
So the elements in [tex]\( A' \)[/tex] are:
[tex]\[
A' = \{2, 3, 5, 6, 8, 9\}
\][/tex]
### Finding the Complement of Set [tex]\( B \)[/tex]:
1. List the elements in set [tex]\( B \)[/tex]:
[tex]\[
B = \{1, 3, 4, 7, 10\}
\][/tex]
2. Identify the elements in [tex]\( U \)[/tex] that are not in [tex]\( B \)[/tex]:
- The elements of [tex]\( U \)[/tex] that are not in [tex]\( B \)[/tex] are:
[tex]\[
\{2, 5, 6, 8, 9\}
\][/tex]
3. The complement of set [tex]\( B \)[/tex] ([tex]\( B' \)[/tex]) consists of these elements:
[tex]\[
B' = \{2, 5, 6, 8, 9\}
\][/tex]
So the elements in [tex]\( B' \)[/tex] are:
[tex]\[
B' = \{2, 5, 6, 8, 9\}
\][/tex]
### Summary:
- Elements in the set [tex]\( A' \)[/tex]:
[tex]\[
A' = \{2, 3, 5, 6, 8, 9\}
\][/tex]
- Elements in the set [tex]\( B' \)[/tex]:
[tex]\[
B' = \{2, 5, 6, 8, 9\}
\][/tex]
