Answered

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Let [tex]\( U = \{1, 2, 3, \ldots, 8, 9, 10\} \)[/tex] be the universal set.

Let sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] be subsets of [tex]\( U \)[/tex], where:

[tex]\[ A = \{1, 4, 7, 10\} \][/tex]
[tex]\[ B = \{1, 3, 4, 7, 10\} \][/tex]

List the elements in the set [tex]\( A^{\prime} \)[/tex]:

[tex]\[ A^{\prime} = \{ \square \} \][/tex]

List the elements in the set [tex]\( B^{\prime} \)[/tex]:

[tex]\[ B^{\prime} = \{ \square \} \][/tex]

Sagot :

GinnyAnswer
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]
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