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Suppose that [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are sets, defined as follows. Find the intersection and union of [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. Enter the elements of the sets in increasing order, separated by commas. If a set is the empty set, just enter DNE inside the braces given.

[tex]\[
\begin{array}{l}
A = \{2, 3, 6, 7\} \text{ and } B = \{1, 2, 3, 6, 7, 8\} \\
A \cap B = \{\square\} \\
A \cup B = \{\square\}
\end{array}
\][/tex]



Answer :

GinnyAnswer
Given the sets [tex]\( A = \{2, 3, 6, 7\} \)[/tex] and [tex]\( B = \{1, 2, 3, 6, 7, 8\} \)[/tex], we need to determine the intersection and union of these sets.

### Intersection ([tex]\(A \cap B\)[/tex]):
The intersection of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are common to both [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

The common elements are [tex]\( 2, 3, 6, \)[/tex] and [tex]\( 7 \)[/tex].

Thus, the intersection [tex]\(A \cap B = \{2, 3, 6, 7\}\)[/tex].

### Union ([tex]\(A \cup B\)[/tex]):
The union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is the set of elements that are in [tex]\( A \)[/tex], in [tex]\( B \)[/tex], or in both.
- Elements in [tex]\( A \)[/tex]: [tex]\( \{2, 3, 6, 7\} \)[/tex]
- Elements in [tex]\( B \)[/tex]: [tex]\( \{1, 2, 3, 6, 7, 8\} \)[/tex]

Combining the elements from both sets (and removing duplicates) gives us: [tex]\( 1, 2, 3, 6, 7, \)[/tex] and [tex]\( 8 \)[/tex].

Thus, the union [tex]\(A \cup B = \{1, 2, 3, 6, 7, 8\}\)[/tex].

### Answer:
[tex]\[ \begin{array}{l} A = \{2, 3, 6, 7\} \\ B = \{1, 2, 3, 6, 7, 8\} \\ A \cap B = \{2, 3, 6, 7\} \\ A \cup B = \{1, 2, 3, 6, 7, 8\} \end{array} \][/tex]

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