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Let [tex]$A=\{0,1,3,5,6\}, B=\{3,5,6,8\}, C=\{0,2,4,5,7,8\}$[/tex].

List the elements of the following sets. If there is more than one element, write them separated by commas.

[tex]\[
\begin{array}{l}
A \cap B = \{3,5,6\} \\
A \cup B = \{0,1,3,5,6,8\} \\
(B \cup C) \cap A = \{\square\} \\
B \cup (C \cap A) = \{\square\}
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's find the elements for each of the sets as specified:

1. Intersection of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] ([tex]\( A \cap B \)[/tex]):
- We look for elements that are common in both sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
- [tex]\( A \cap B = \{3, 5, 6\} \)[/tex].

2. Union of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] ([tex]\( A \cup B \)[/tex]):
- We combine all elements from sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], without duplicates.
- [tex]\( A \cup B = \{0, 1, 3, 5, 6, 8\} \)[/tex].

3. Intersection of the Union of [tex]\( B \)[/tex] and [tex]\( C \)[/tex] with [tex]\( A \)[/tex] [tex]\((B \cup C) \cap A\)[/tex]:
- First, find the union of [tex]\( B \)[/tex] and [tex]\( C \)[/tex]: [tex]\( B \cup C = \{0, 2, 3, 4, 5, 6, 7, 8\} \)[/tex].
- Then find the intersection of this union with [tex]\( A \)[/tex]:
- Elements in [tex]\( A \)[/tex]: \{0, 1, 3, 5, 6\}
- Intersection: \{0, 3, 5, 6\}
- Therefore, [tex]\((B \cup C) \cap A = \{0, 3, 5, 6\} \)[/tex].

4. Union of [tex]\( B \)[/tex] with the Intersection of [tex]\( C \)[/tex] and [tex]\( A \)[/tex] [tex]\(B \cup (C \cap A)\)[/tex]:
- First, find the intersection of [tex]\( C \)[/tex] and [tex]\( A \)[/tex]: [tex]\( C \cap A = \{0, 5\} \)[/tex].
- Then find the union of [tex]\( B \)[/tex] with this intersection:
- Elements in [tex]\( B \)[/tex]: \{3, 5, 6, 8\}
- Union: \{0, 3, 5, 6, 8\}
- Therefore, [tex]\( B \cup (C \cap A) = \{0, 3, 5, 6, 8\} \)[/tex].

Hence, the solutions for the given sets are:

[tex]\[ \begin{aligned} &A \cap B = \{3, 5, 6\}, \\ &A \cup B = \{0, 1, 3, 5, 6, 8\}, \\ &(B \cup C) \cap A = \{0, 3, 5, 6\}, \\ &B \cup (C \cap A) = \{0, 3, 5, 6, 8\}. \end{aligned} \][/tex]
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